83 free MCQs on Motion in a Plane, each with its own worked answer and explanation. Vectors, projectile motion, uniform circular motion, and relative velocity - the foundation of 2D kinematics for NEET and JEE.
Take the timed Motion in a Plane chapterwise test →83 practice questions on Motion in a Plane, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Motion in a Plane notes.
Projectiles at equal speed: range is maximum at 45°, and complementary angles (30° and 60°) share the same range. Image: Cmglee, CC BY-SA 3.0, via Wikimedia Commons.
Q1.
The minimum number of coplanar vectors of unequal magnitude needed to give a zero resultant is:
Q2.
The dot (scalar) product of two mutually perpendicular vectors is:
Q3.
During projectile motion (neglecting air resistance), the acceleration of the projectile is:
Q4.
The angle between the velocity and the centripetal acceleration of a body in uniform circular motion is:
Q5.
When two vectors are anti-parallel, the angle between them is:
Q6.
A stone is thrown vertically upward. At the highest point, its velocity is:
Q7.
A car decelerates from 20 m/s to rest in 4 seconds. Its deceleration is:
Q8.
Relative velocity of a body A with respect to B is given by:
Q9.
A runner completes one full lap around a circular track of radius R. The displacement is:
Q10.
A body starts from rest and travels 45 m in 3 seconds with uniform acceleration. The acceleration is:
Q11.
If a body moves with constant speed in a circular path, what changes?
Q12.
A body moving at 10 m/s is brought to rest by a constant force. If deceleration is 2 m/s², the time taken is:
Q13.
Which graph represents uniform acceleration?
Q14.
A projectile is launched horizontally. Which component of its velocity remains constant throughout?
Q15.
An athlete runs 400 m around a track and returns to the start. Distance covered is:
Q16.
A ball is thrown horizontally from a height h. The time to reach the ground depends on:
Q17.
A physical quantity having both magnitude and direction is a:
Q18.
The resultant of two vectors is commonly found using the:
Q19.
The magnitude of any vector is always:
Q21.
Projectile motion takes place in:
Q22.
The horizontal component of a projectile’s velocity is:
Q23.
The trajectory (path) of a projectile is a:
Q24.
The acceleration of a projectile is directed:
Q25.
Two vectors are equal when they have the same magnitude and the same:
Q26.
A projectile reaches a maximum height of 30 m and lands 60 m from the launch point. The tangent of its angle of projection is:
Q27.
A ball is projected with speed 20 m s<sup>-1</sup> at 30° to the horizontal. Its time of flight is (g = 10 m s<sup>-2</sup>):
Q28.
Two vectors of magnitudes 5 and 12 act at right angles to each other. The magnitude of their resultant is:
Q29.
A projectile has range R when fired at 15°. The same speed gives the same range when fired at an angle of:
Q30.
A body moves in a circle of radius 0.5 m with angular velocity 4 rad s<sup>-1</sup>. Its linear speed is:
Q31.
A particle moves with initial velocity 5 m/s and constant acceleration 2 m/s². How far does it travel in the 4th second?
Q32.
A projectile is launched at 45° with speed 20 m/s. Its horizontal range is (g=10 m/s²):
Q33.
Two trains approach each other on parallel tracks at 80 km/h and 60 km/h. Their relative speed is:
Q34.
A stone dropped from height h hits the ground with speed v. From what height should it be dropped to hit with speed 2v?
Q35.
A projectile is fired at angle θ. For what angle is the horizontal range maximum?
Q36.
A train 200 m long passes a pole in 10 s. Time to pass a platform 300 m long is:
Q37.
A particle is thrown vertically with speed u. The ratio of max height to range when launched at 45° is:
Q38.
Two balls are thrown simultaneously: one vertically up at 20 m/s, one dropped from 80 m height. When do they meet? (g=10 m/s²)
Q39.
A river flows east at 4 m/s. A swimmer swims north at 3 m/s relative to water. His resultant velocity magnitude is:
Q40.
A ball is thrown from a building 80 m high with horizontal speed 10 m/s. Horizontal range when it hits ground is (g=10):
Q41.
Deceleration of a particle is given by a = -kv. This means deceleration is proportional to:
Q42.
A particle executes uniform circular motion. Which statement is correct?
Q43.
From the top of a tower 45 m high, a stone is thrown horizontally at 20 m/s. Velocity on reaching ground (g=10):
Q44.
A particle is projected at angle α above horizontal. Time of flight equals:
Q45.
The horizontal range of a projectile is maximum for a launch angle of:
Q46.
At the highest point of its path, a projectile’s vertical velocity component is:
Q47.
For a projectile launched at speed u and angle θ, the time of flight is:
Q48.
In uniform circular motion the speed is constant, but the ___ keeps changing:
Q49.
In uniform circular motion, the acceleration is directed toward the:
Q50.
Two projectiles launched at complementary angles (θ and 90° − θ) with the same speed have the same:
Q51.
A swimmer whose speed relative to water is 6 m/s must cross a 60 m wide river flowing at 3 m/s and reach the point directly opposite. He should aim upstream, measured from the line straight across, at an angle of:
Q52.
A particle moves in a circle of radius 4 m. Its speed is 4 m s<sup>-1</sup> and increasing at 3 m s<sup>-2</sup>. The magnitude of its net acceleration at that instant is:
Q53.
Two balls are thrown with the same speed at 30° and 60° to the horizontal. The ratio of their times of flight (30° : 60°) is:
Q54.
A boat heads straight across a 300 m wide river at 5 m s<sup>-1</sup> relative to the water, while the river flows at 4 m s<sup>-1</sup>. The downstream drift when it reaches the far bank is:
Q55.
Rain falls vertically at 10 m s<sup>-1</sup>. A man runs horizontally at 10 m s<sup>-1</sup>. To keep dry he should tilt his umbrella from the vertical by:
Q56.
A stone is projected from ground at angle 37° with 50 m/s. Time to reach max height (sin37°=0.6, g=10):
Q57.
A particle has displacement x = A·sin(ωt). Its maximum velocity is:
Q58.
Two cars start from rest at same point and move in same direction. Car A accelerates at 4 m/s² and Car B at 2 m/s². After 10 s, separation between them is:
Q59.
A particle moves along x-axis such that acceleration = -ω²x. This represents:
Q60.
A man walks at 6 km/h due east, rain falls at 8 km/h vertically. Relative velocity of rain with respect to man:
Q61.
Displacement of a particle is x = t³ - 3t + 2. When is the particle momentarily at rest?
Q62.
A ball is thrown upward from ground. It reaches height 5 m at t=1 s and again at t=3 s. Initial speed is (g=10):
Q63.
Minimum speed during projectile motion at angle θ (initial speed u) is:
Q64.
A particle travels 20 m in the first 5 seconds and 30 m in next 5 seconds. Acceleration is uniform. Acceleration is:
Q65.
A shell is fired at 30° angle with speed 60 m/s. At highest point, it explodes into two equal pieces. One piece falls vertically. Speed of other piece is (g=10):
Q66.
For a particle in uniform circular motion of radius R and speed v, centripetal acceleration is directed:
Q67.
Two particles are simultaneously projected from same point: one horizontally at v, other vertically at v. Time for their velocity vectors to become perpendicular is (g=10):
Q68.
A projectile is launched at 20 m/s at 30° to the horizontal. Its range is (g = 10 m/s²):
Q69.
The centripetal acceleration of a body moving at speed v in a circle of radius r is:
Q70.
A stone whirled in a horizontal circle of radius 2 m at 4 m/s has a centripetal acceleration of:
Q71.
The maximum height reached by a projectile launched at speed u and angle θ is:
Q72.
Two perpendicular vectors of magnitudes 3 and 4 have a resultant of magnitude:
Q73.
The horizontal range of a projectile equals its maximum height when tanθ equals:
Q74.
In projectile motion, the horizontal and vertical motions are:
Q75.
For a body in circular motion, angular velocity ω, speed v and radius r are related by:
Q76.
Two projectiles are fired with the same speed at 30° and 60°. The ratio of their maximum heights (30° : 60°) is:
Q77.
For a projectile, the maximum height equals the horizontal range. The angle of projection satisfies:
Q78.
A river is 400 m wide flowing at 3 m/s. A swimmer swims at 5 m/s relative to water and wishes to cross straight across (shortest path). The time to cross is:
Q79.
Car A moves east at 3 m/s and car B moves north at 4 m/s. The speed of A relative to B is:
Q80.
A projectile is launched at 20 m/s at 60° above the horizontal. Its speed at the highest point of the trajectory is:
Q81.
A particle in uniform circular motion at speed 10 m/s turns through a quarter circle. The magnitude of its change in velocity is:
Q82.
A stone is thrown horizontally at 15 m/s from a tower 20 m high (g = 10 m/s²). Its horizontal range on the ground is:
Q83.
For a particle in uniform circular motion, the ratio of its average speed to the magnitude of its average velocity over half a revolution is:
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