Kinematics — practice questions
189 curated practice questions from Kinematics (Physics JEE Advanced, NTA Exams) — 58 medium, 131 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.
- Let and c = i + j -2 k be three vectors. A vector in the plane of and whose projection on is of magnitude 2 3 is
- A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t =…
- A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t =…
- Let x , y ext and z be three vectors each of magnitude and the angle between each pair of them is π/3. If is a non-zero…
- A drag racing car starts from rest at t = 0 and moves along a straight line with velocity given by v = bt2, where b is…
- Assertion: Plotting the acceleration–time graph from a given position–time graph of a particle moving along a straight…
- In 1.0 s, a particle goes from point A to point B, moving in a semicircle (as shown in the figure). The magnitude of…
- If a =( i + j + k ), a b =1 and a b = j - k , then b is
- From an inclined plane two particles are projected with same speed at same angle , one up and other down the plane as…
- Look at the graphs (a) to (d) carefully and indicate which of these possible represents one dimensional motion of a…
- Let ∆ PQR be a triangle. Let a = QR , b = RP and c = PQ . If | a |=12,| b |=4 3 and b c =24, then which of the…
- The displacement (x) of a particle depends on time (t) as x= t^ 2 - t^ 3
- A particle is moving along X–axis whose acceleration is given by a = 3x – 4, where x is the location of the particle…
- Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that…
- A ball is dropped from the top of a tower in a high-speed wind. The wind exerts a steady force on the ball. The path…
- Two cars are moving in the same direction with the same speed of 30 km/h. They are separated by 5 km. What is the speed…
- A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended…
- If velocity of the particle is given by v= x , where x denotes the position of the particle and initially particle was…
- A body starts from rest moves along a straight line with constant acceleration. The variation of speed v with distance…
- The number of unit vectors perpendicular to = (1, 1, 0) and = (0, 1, 1) is
- A particle is moving with velocity of 4 m/s along + ve X direction, an acceleration of 1 m/s2 is acted on the particle…
- A particle moves along a straight line such that its displacement at any time t is given by: s = (t3 – 3t2 + 2) m. The…
- Let two non-collinear unit vectors and form an acute angle. A point P moves so that at any time t the position vector…
- Velocity and acceleration of a particle initially are v =(3 i +4 j ) m/s and a =-(6 i +8 j ) m/s2 respectively…
- Let and be two non-collinear unit vectors. If u = a -( a b ) b ext and v = a imes b , then | | is
- A particle moves in the x-y plane according to the law x = kt and y =kt (1 – at), where k and a are positive constants…
- Two projectiles A and B are projected with same speed and angle of projection 30° for the projectile A and 45° for the…
- Let a , b , c be unit vectors such that Which one of the following is correct?
- A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first…
- A particle is moving eastwards with a velocity of 5 m/s. In 10 s the velocity changes to 5 m/s northwards. The average…
- .A body moving with a uniform acceleration has velocities of u and v when passing through points A and B in its path…
- An aircraft moving with a speed of 250 m/s is at a height of 6000 m, just overhead of an anti-aircraft gun. The time…
- Assertion: Two stones are simultaneously projected from level ground from same point with same speeds but different…
- A body of mass m is thrown upwards at an angle with the horizontal with velocity v. While rising up the velocity of the…
- A river is flowing from west to east at a speed of 20 m/min. A man on the south bank of the river, capable of swimming…
- From the top of a tower two stones, whose masses are in the ratio 1:2 are thrown one straight up with an initial speed…
- A cricketer hits a ball with a velocity 25 m/s at 60o above the horizontal. How far (approximately) above the ground it…
- The velocity v and displacement r of a body are related as v2 = kr, where k is a constant. What will be the velocity…
- ext Let a = i + j + k , b = i - j + k ext and c = i - j - k be three vectors. A vector in the plane of a ext and b …
- Three vectors P , Q ext and R areshown in the figure. Let S be any point on the vector . The distance between the…
- A small block of mass M moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the…
- A person standing near the edge of the top of a building throws two balls A and B. The ball A is thrown vertically…
- A particle of mass m is projected from the ground with an initial speed u 0 at an angle α with the horizontal. At the…
- Two particles A and B are projected simultaneously from a point situated on a horizontal plane. The particle A is…
- At a distance of 500 m from the traffic light, brakes are applied to an automobile moving at a velocity of 20 m/s. The…
- A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The…
- A particle moves in the X-Y plane under the influence of a force such that its linear momentum is p (t)=A[ i (k t)- j…
- A river is flowing from West to East at a speed of 5 metres per minute. A man on the south bank of the river, capable…
- Assertion: In order to hit a target, a man should point his rifle in the same direction as target. Reason: The…
- If are non coplanar unit vectors such that then the angle between a ext and b is
- In projectile motion, the modulus of rate of change of speed
- The equation of motion of a projectile is y=12 x- 3 4 x^ 2 . Given that g =10 ms–2, what is the range of the projectile
- Two trains are each 50 m long starts moving parallel towards each other at speeds 10 m/s and 15 m/s respectively, after…
- Two particles A and B are moving along x–axis whose position–time graphs are as shown in the figure below. Mark the…
- A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At…
- A particle is projected at an angle of 60o above the horizontal with a speed of 10 m/s. After some time the direction…
- A projectile is thrown in the upward direction making an angle of 60^ with the horizontal direction with a velocity of…
- Let P , Q , R and S be the points on the plane with position vectors -2 i - j , 4 i , 3 i +3 j and -3 i +2 j…
- y ( x, t ) = 0.8/[(4 x + 5 t ) 2 + 5] represents a moving pulse, where x and y are in metre and t in second. Then
- Three particles A, B and C are thrown from the top of a tower 100 m in height with the same speed 10 m/s. A is thrown…
- A particle A is projected vertically upwards. Another particle B of same mass is projected at an angle of 45o. Both…
- A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of…
- If a , b and c are unit vectors, then | a - b |^ 2 +| b - c |^ 2 +| c - a |^ 2 does not exceed
- The rowing speed of a man relative to water is 5 km/h and the speed of water flow is 3 km/h. At what angle to the river…
- A body is projected with velocity v1 from the point A as shown in figure. At the same time, another body is projected…
- A particle moving along a straight line with uniform acceleration has velocities 7 m/s at P and 17 m/s at Q. R is the…
- A projectile is projected at an angle of 15° to the horizontal with some speed v. If another projectile is projected…
- A horizontal wind is blowing with a velocity v towards north-east. A man starts running towards north with acceleration…
- A particle moves with an initial velocity v0 and retardation , where v is its velocity at any time t.
- A particle P is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously another…
- A stone is thrown vertically upward with an initial velocity v0. The distance travelled in time 4v0/3g is
- Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit…
- The displacement of a particle after time t is given by x = (k/b2) (1 – e–bt), where b is a constant. What is the…
- A student skates up a ramp that makes an angle 30° with the horizontal. He/she starts (as shown in the figure) at the…
- A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of…
- A particle has an initial velocity of 3 i +4 j and an acceleration of 0.4 i +0.3 j . Its speed after 10 s is:
- Four particles are moving along X–axis. Their coordinates (in metres) as function of time (in seconds) are given by x1…
- A projectile is fired at an angle of 30o to the horizontal such that the vertical component of its initial velocity is…
- From the top of a tower of height 40 m a ball is projected upwards with a speed of 20 m/s at an angle of elevation of…
- A fielder in a cricket match throws a ball from the boundary line to the wicket keeper. The ball describes a parabolic…
- A lift is going up from the ground. The variation in the speed of the lift is as given in the graph. What is the height…
- A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The displacement of the stone from the…
- A particle is projected from the ground with an initial speed of u at an angle with horizontal. The average velocity of…
- An aircraft moving with a speed of 250 m/s is at a height of 6000 m, just overhead of an anti-aircraft gun. If the…
- The position vector of a particle is given as i = ( t ^ 2 -4 t +6 ) i + ( t ^ 2 ) j The time after which the velocity…
- The velocity–displacement curve for an object moving along a straight line is shown in the figure below. At which of…
- A particle has a rectilinear motion and the figure gives its displacement as a function of time. Which of the following…
- Assertion: In a plane to plane projectile motion, the angle between instantaneous velocity vector and acceleration…
- An aeroplane is flying at a constant horizontal velocity of 600 km/h at an elevation of 6 km towards a point directly…
- A particle is dropped under gravity from rest from a height h(g = 9.8 m/sec 2 ) and it travels a distance 9h/25 in the…
- A vector has components 2 p and 1 with respect to a rectangular cartesian system. This system is rotated through a…
- Two particles A and B are moving along straight line, whose position–time graph is a shown in the figure below…
- A ball is projected horizontally with a speed v from the top of a plane inclined at an angle 45° with the horizontal…
- For non zero vectors a , b , c , |( a b ) c |=| a || b || c | holds if and only if
- A wheel with radius 45 cm rolls without slipping along a horizontal floor as shown in figure. P is a dot pointed on the…
- We know how by neglecting the air resistance, the problems of projectile motion can be easily solved and analysed. Now…
- A body is projected at an angle of 30° with the horizontal with speed 30 m/s. What is the angle with the horizontal…
- A body is thrown horizontally with a velocity 2 g h from the top of a tower of height h. It strikes the level ground…
- Assertion: When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same…
- The coordinates of a particle moving in a plane are given by x ( t ) = a cos( pt ) and y ( t ) = b sin( pt ) where a, b…
- A particle is projected up an inclined plane with initial speed v = 20 m/s at an angle =30^ with plane. The component…
- The center of a disk of radius r and mass m is attached to a spring of spring constant k , inside a ring of radius R >…
- An object moving along a straight line has a constant acceleration of 4 m/s2. The position–time graph for this object…
- A projectile is thrown at an angle of 40o with the horizontal and its range is R1. Another projectile is thrown at an…
- Let the vectors P Q , Q R , R S , S T , T U and U P represent the sides of a regular hexagon. Statement-1 : P Q ( R S +…
- A small but heavy block of mass 10 kg is attached to a wire 0.3m long. Its breaking stress is 4.8 × 10 7 N/m 2 . The…
- Consider a boy on a trolley who throws a ball with speed 20 m/s with respect to ground at an angle 37° with vertical…
- Statement - 1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to…
- The velocity of a particle moving along x–axis is given as v = x2 – 5x + 4 (in m/s) where x denotes the x–coordinate of…
- A person walks up a stationary escalator in time t1. If he remains stationary on the moving escalator, then it can take…
- Position vector of a particle moving in x-y plane at time t is: r =a(1- t) i +a t j The path of the particle is
- Starting at time t = 0 from the origin with speed 1 m s −1 , a particle follows a two-dimensional trajectory in the x …
- Which of the following statements are true for a moving body?
- On a calm day a boat can go across a lake and return in time T0 at a speed v. On a rough day there is uniform current…
- A particle of mass m is moving in the xy -plane such that its velocity at a point ( x , y ) is given as v = (y x +2 x y…
- The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding…
- A particle is projected from a point (0, 1) on Y–axis (assume + Y direction vertically upwards) aiming towards a point…
- Let u =u_ 1 i +u_ 2 j +u_ 3 k be a unit vector in R 3 and w = 1 6 ( i + j +2 k ) . Given that there exists a vector in…
- A particle is projected with a speed V from a point O making an angle of 30o with the vertical. At the same instant, a…
- A particle of mass m moves on the x -axis as follows: It starts from rest at t = 0 from the point x = 0, and comes to…
- A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a…
- Assertion: When velocity of a particle is zero then acceleration of a particle is also zero. Reason: Acceleration is…
- A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t =…
- Let α, β, γ be distinct real numbers. The points with position vectors i + j + k , i + j + k , i + j + k
- A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity…
- Three identical balls are thrown with same speed at angles of 15o, 45o and 75o with the horizontal respectively. The…
- A stone is released from a high-flying balloon that is descending at a constant speed of 10 m/s. After 20 s of…
- A balloon starts rising from the ground with an acceleration of 1.25 m/s2 after 8s, a stone is released from the…
- We know how by neglecting the air resistance, the problems of projectile motion can be easily solved and analysed. Now…
- When a ball is thrown up vertically with velocity V 0 , it reaches a maximum height of ‘h’. If one wishes to triple the…
- If the vectors a , b and or the sides BC , CA and AB respectively of a triangle ABC , then
- The acceleration of an object, starting from rest and moving along a straight line is as shown in the figure below…
- If a , b , c are three non-zero non-coplanar vectors and b _ 1 = b - a b | a |^ 2 a , b _ 2 = b + a b | a |^ 2 a c _ 1…
- A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10s is x1. next 10s…
- For three vectors u , v , w which of the following expression is not equal to any of the remaining three
- For 3 particles A, B and C moving along x–axis, x–t graph is as shown below. Mark out the correct relationships between…
- A small block slides, without friction, down an inclined plane starting from rest. Let S n be the distance travelled…
- The vector 1 3 (2 i -2 j + k ) is
- Two particles A and B are moving along x–axis whose position–time graphs are as shown in the figure below. For the time…
- A bird flies for 4s with a velocity of (t–2) m/s in a straight line, where t = time in seconds. It covers a distance of
- If the displacement of a particle varies with time as x = t + 7, the
- Let O be the origin and O A =2 i +2 j + k , O B = -2 +2 k and O C = 1 2 ( O B - O A ) for some λ > 0. If | O B O C |= 9…
- Assertion: Magnitude of average velocity is equal to average speed. Reason: Magnitude of instantaneous velocity is…
- A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of…
- A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound…
- The displacement–time graph of a moving particle is shown in figure. The instantaneous velocity of the particle is…
- A boat which has a speed of 5 km/h in still water crosses a river of width 1 km along the shortest possible path in 15…
- The trajectory of a projectile in a vertical plane is y = ax – bx2, where a and b are constants and x and y are…
- As a rocket is accelerating vertically upwards at 9.8 m/s2 near the earth’s surface, it releases a projectile…
- A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit –φ…
- Assertion: A particle moves in a straight line with constant acceleration. The average velocity of this particle cannot…
- In 1.0 s, a particle goes from point A to point B , moving in a semicircle of radius 1.0 m as shown in the figure. The…
- A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube…
- Time taken by an object falling from rest to cover the height of h 1 and h 2 is respectively t1 and t2 then the ratio…
- A body A is projected upwards with a velocity of 98 m/s. a second body B is projected upwards with the same initial…
- If a and b are vectors such that | a + b |= 29 and a (2 i +3 j +4 k )=(2 i +3 j +4 k ) b . then a possible value of ( a…
- Two men A and B, A standing on the extended floor nearby a building and B is standing on the roof of the building. Both…
- There are two values of time for which a projectile is at the same height. The sum of these two times is equal to
- Let v and a denote the velocity and acceleration respectively of a particle moving in a circular path then,
- A body is projected horizontally with speed 20 m/s from top of a tower. What will be its speed nearly after 5 sec? Take…
- Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight…
- A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the…
- A body is projected horizontally with speed 20 m/s from top of a tower, what will be the displacement of the body if it…
- A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance…
- From the top of a tower 19.6 m high, a ball is thrown horizontally. If the line joining the point of projection to the…
- Assertion: For a particle moving along a straight line or in a plane, the average velocity vector over a time interval…
- The velocity displacement graph of a particle moving along a straight line is shown. The most suitable…
- A particle moves in x-y plane. The position vector of particle at any time t is r = (2 t ) i + (2 t ^ 2 ) j m . The…
- An elevator is moving upwards with constant acceleration. The broken curve shows the position y of the ceiling of the…
- A particle A is projected from the ground with an initial velocity of 10 m/s at an angle of 60o with horizontal. From…
- From certain height, two bodies are projected horizontally with velocities 10 m/s and 20 m/s. They hit the ground in t1…
- A ball of mass ( m ) 0.5 kg is attached to the end of a string having length ( L ) 0.5 m. The ball is rotated on a…
- Assertion: Two particles of different mass, projected with same velocity and angle of projection, the maximum height…
- Let a = i +2 j + k , b = i - j + k ext and c = i + j - k A vector in the plane of a ext and b whose projection on is is
- What determines the nature of the path followed by a particle?
- From a point on the ground at a distance 2 metres from the foot of a vertical wall, a ball is thrown at an angle of 45o…
- A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height…
- A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t =…
- We know how by neglecting the air resistance, the problems of projectile motion can be easily solved and analysed. Now…
- We know how by neglecting the air resistance, the problems of projectile motion can be easily solved and analysed. Now…
- A particle is projected vertically upwards with a velocity u from a point O. When it returns to the point of projection:
- Let be vectors such that u + v + w =0 . If | u |=3,| v |=4 ext and | w |=5, then u v + v w + w u is
- A rocket is fired upwards from earth’s surface such that it creates an acceleration of 20 ~ms ^ -2 . If after 5 sec…
- A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at t =…
- An object moves along the x–axis. Its x coordinate is given as a function of time as x = 7 t – 3t2 where x is in metre…
- A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0 . At this instant of…
- An object is thrown in vertically upward direction. During its rising
- A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the…
- A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is