Work on paper, not in your head. Draw before you calculate — every question here rewards it, and several are much harder without a diagram.

1.  A body travels along a straight line. It covers the first half of the total distance with a speed of 30 km/h and the second half with 60 km/h. The average speed of the body for the entire journey is:

(A)  40 km/h

(B)  45 km/h

(C)  50 km/h

(D)  35 km/h

2.  A particle starts from rest and moves with a uniform acceleration of 2 m/s². The ratio of the distances covered by it in the 3^(rd) second and the 5^(th) second is:

(A)  3 : 5

(B)  5 : 9

(C)  9 : 25

(D)  1 : 2

3.  A car moving at 20 m/s is brought to rest over a stopping distance of 40 m by applying brakes. If the speed of the car is doubled, the stopping distance under the same deceleration will be:

(A)  80 m

(B)  120 m

(C)  160 m

(D)  200 m

4.  A stone dropped from the top of a tower reaches the ground in 4 s. Taking g = 10 m/s², the height of the tower is:

(A)  40 m

(B)  80 m

(C)  120 m

(D)  160 m

5.  A ball is thrown vertically upward with a speed of 20 m/s. The magnitude of its displacement after 3 s is (g = 10 m/s²):

(A)  15 m

(B)  20 m

(C)  25 m

(D)  45 m

6.  A particle moves along the x-axis with x = t² − 6t + 8, where x is in metres and t in seconds. The position of the particle at the instant its velocity becomes zero is:

(A)  −1 m

(B)  0 m

(C)  3 m

(D)  8 m

7.  The position–time graph of a particle is a straight line with a negative slope. Which statement is correct?

(A)  The particle moves in the negative direction with constant speed

(B)  The particle moves in the positive direction and slows down

(C)  The particle is at rest

(D)  The particle has a constant negative acceleration

8.  The area under the velocity-time (v-t) graph for a particle moving in a straight line represents its:

(A)  Acceleration

(B)  Displacement

(C)  Force

(D)  Rate of change of acceleration

9.  A bullet is fired horizontally from a height of 490 m above the ground with a horizontal velocity of 100 m/s. The time taken by the bullet to hit the ground is (g = 9.8 m/s²):

(A)  5 s

(B)  10 s

(C)  20 s

(D)  50 s

10.  Two objects are projected at angles of 30^(∘) and 60^(∘) with the horizontal with the same initial velocity u. The ratio of their horizontal ranges is:

(A)  1 : 1

(B)  1:√(3)

(C)  √(3):1

(D)  1 : 3

11.  For a projectile thrown at an angle θ to the horizontal, the ratio of maximum height H to the square of time of flight T² depends on:

(A)  Initial velocity u only

(B)  Acceleration due to gravity g only

(C)  Angle of projection θ only

(D)  Both u and θ

12.  A swimmer can swim in still water at 4 km/h. If he crosses a river flowing at 3 km/h along the shortest path, the direction in which he must stroke relative to the river flow is:

(A)  90^(∘)

(B)  120^(∘)

(C)  138.6^(∘)

(D)  150^(∘)

13.  Rain is falling vertically downward at 10 m/s. A person moves horizontally at 10 m/s. The magnitude of relative velocity of rain with respect to the person is:

(A)  0 m/s

(B)  10 m/s

(C)  10√(2)~m/s

(D)  20 m/s

14.  A train 200 m long is moving with a constant speed of 20 m/s. Time taken by it to completely cross a bridge of length 800 m is:

(A)  10 s

(B)  30 s

(C)  40 s

(D)  50 s

15.  A particle moves in a circular path of radius 2 m with a constant speed of 4 m/s. The magnitude of centripetal acceleration is:

(A)  2 m/s²

(B)  4 m/s²

(C)  8 m/s²

(D)  16 m/s²

16.  The angular speed of the second hand of a standard mechanical clock is:

(A)  (π)/(30)~rad/s

(B)  (π)/(60)~rad/s

(C)  (π)/(1800)~rad/s

(D)  2π rad/s

17.  If the displacement of a body is proportional to the square of time (s ∝ t²), the body is moving with:

(A)  Uniform velocity

(B)  Uniform acceleration

(C)  Increasing acceleration

(D)  Decreasing acceleration

18.  A ball dropped from a height h rebounds from the floor to a height h/4. The fraction of velocity lost upon impact is:

(A)  1/4

(B)  1/2

(C)  3/4

(D)  1/√(2)

19.  A body thrown vertically upward reaches a maximum height H. Its speed at height 3H/4 is:

(A)  (u)/(2)

(B)  (u)/(√(2))

(C)  (u)/(4)

(D)  (√(3)u)/(2)

20.  The angle of projection of a projectile for which its horizontal range R is equal to maximum height H is:

(A)  tan⁻¹(1)

(B)  tan⁻¹(2)

(C)  tan⁻¹(4)

(D)  tan⁻¹(0.5)

21.  A body starts from rest and moves along a straight line with uniform acceleration. The ratio of displacements in successive equal intervals of time T is:

(A)  1 : 2 : 3 : 4

(B)  1 : 3 : 5 : 7

(C)  1 : 4 : 9 : 16

(D)  1 : 1 : 1 : 1

22.  A vector trajectory is given by x = 3t and y = 4t. The nature of the path followed by the particle is:

(A)  Parabola

(B)  Circle

(C)  Straight line passing through origin

(D)  Ellipse

23.  The position x of a particle varies with time t as x = at² − bt³. The acceleration of the particle will be zero at time t equal to:

(A)  (a)/(3b)

(B)  (a)/(2b)

(C)  (2a)/(3b)

(D)  Zero

24.  The velocity of a particle at time t = 0 is u = 10 m/s. It experiences a deceleration given by a = − 2v. The time after which its velocity drops to 5 m/s is:

(A)  (1)/(2)ln 2

(B)  ln 2

(C)  2ln 2

(D)  (1)/(4)ln 2

25.  Two cars A and B are traveling in the same direction on a straight road with speeds 15 m/s and 10 m/s, respectively. The velocity of car A relative to car B is:

(A)  25 m/s

(B)  5 m/s

(C)  − 5 m/s

(D)  150 m/s

26.  A stone is thrown horizontally from a cliff of height 20 m with speed 15 m/s. The speed with which it strikes the ground is (g = 10 m/s²):

(A)  15 m/s

(B)  20 m/s

(C)  25 m/s

(D)  35 m/s

27.  A particle performing uniform circular motion completes 120 revolutions per minute in a circle of radius 0.5 m. Its linear speed is:

(A)  π m/s

(B)  2π m/s

(C)  4π m/s

(D)  0.5π m/s

28.  The displacement-time graph of a body is parallel to the time axis. This indicates that the body is:

(A)  Moving with uniform speed

(B)  Moving with uniform acceleration

(C)  At rest

(D)  In free fall

29.  A stone is dropped into a well of depth 45 m. If the speed of sound in air is 330 m/s, the sound of splash is heard after (g = 10 m/s²):

(A)  3.0 s

(B)  3.14 s

(C)  3.5 s

(D)  4.0 s

30.  A body starts from rest and accelerates uniformly at 2 m/s² for 5 s. It then travels at constant velocity for a further 10 s. The total distance travelled is:

(A)  25 m

(B)  100 m

(C)  125 m

(D)  150 m

31.  A particle is moving along a circle of radius R with constant angular speed ω. Its centripetal acceleration is directed:

(A)  Tangentially in direction of motion

(B)  Tangentially opposite to motion

(C)  Radially inward toward center

(D)  Radially outward from center

32.  The maximum range of a projectile fired with velocity u is R_(max). The maximum height attained during this flight is:

(A)  R_(max)

(B)  R_(max)/2

(C)  R_(max)/4

(D)  2R_(max)

33.  The velocity vector of a particle is v = (6î+8ĵ) m/s. Its speed is:

(A)  10 m/s

(B)  14 m/s

(C)  2 m/s

(D)  48 m/s

34.  The displacement of a particle is given by y = Asin (ωt). The maximum velocity of the particle is:

(A)  Aω²

(B)  Aω

(C)  (A)/(ω)

(D)  Zero

35.  A particle travels 10 m in 1^(st) second, 20 m in 2^(nd) second, and 30 m in 3^(rd) second under uniform acceleration. Its acceleration is:

(A)  5 m/s²

(B)  10 m/s²

(C)  15 m/s²

(D)  20 m/s²

36.  A projectile reaches its highest point in 3 s. The total time of flight for this projectile is:

(A)  3 s

(B)  4.5 s

(C)  6 s

(D)  9 s

37.  Which quantity remains constant for a projectile during its parabolic trajectory in a uniform gravitational field (ignoring air resistance)?

(A)  Vertical component of velocity

(B)  Horizontal component of velocity

(C)  Kinetic energy

(D)  Total velocity vector

38.  The position-time graph of two objects P and Q make angles of 45^(∘) and 30^(∘) with the time axis. The ratio of their speeds v_(P) : v_(Q) is:

(A)  1:√(3)

(B)  √(3):1

(C)  1 : 1

(D)  1 : 2

39.  A wheel rotates at 300 rpm. Its angular velocity in rad/s is:

(A)  10π

(B)  20π

(C)  30π

(D)  5π

40.  An elevator is moving downward with an acceleration a = g. An object dropped inside the elevator relative to an observer inside it will:

(A)  Fall with acceleration g

(B)  Fall with acceleration 2g

(C)  Remain floating at rest or move with constant speed

(D)  Accelerate upward

If your answer isn’t there

No answers are given, deliberately — and no question tells you which part it comes from, because deciding that is most of the work. If one defeats you, K16 maps twelve physical questions to the tool each one needs. Working it out a second time teaches more than checking a key.

But if you have worked carefully and your answer matches none of the options, it could be our mistake rather than yours. Every question was checked before publication, and checking is not the same as being right.

Those are the questions worth staying with. Rework them, and argue them out with a friend or a teacher. Showing that none of four options can be right is harder physics than picking the one that is — it needs you to trust your own derivation rather than search a menu for something familiar. A student who can do that has understood the motion.

Then tell us, and we will look at it properly. If the question is wrong we will correct it and say so on this page.