Several of these give a constraint as an equation rather than a picture — x_A + 2y_B = L, and the like. There is no pulley rule to recall. Differentiate the relation and read off the answer.

Others ask what a motion looks like from a frame that is itself moving. Decide which frame you are in before you write anything down.

1.  Frame S’ moves relative to Frame S with constant velocity V₀ = 3i − 2j m/s. At t = 0, origins coincide. A particle’s position in S is r(t) = (5t²+2)i + (3t−1)j m. The displacement vector of the particle from t = 1 s to t = 3 s evaluated in Frame S’ is:

(A)  34i + 2j m

(B)  40i + 6j m

(C)  34i + 10j m

(D)  46i + 10j m

2.  A particle moves along a plane curve with position vector r(t) = acos (ωt)i + bsin (ωt)j. The angle between acceleration a(t) and position vector r(t) at any instant t is:

(A)  0°

(B)  45°

(C)  90°

(D)  180°

3.  Two particles A and B move in uniform circular motion on concentric circles of radii r_(A) = 2 m and r_(B) = 8 m with speeds v_(A) = 4 m/s and v_(B) = 8 m/s respectively. The ratio of their centripetal accelerations a_(A)/a_(B) is:

(A)  1 : 1

(B)  1 : 2

(C)  2 : 1

(D)  1 : 4

4.  A body starts from rest at x = 0 and moves with velocity-position relation v = k√(x) where k is a positive constant. The acceleration of the body is:

(A)  k²x

(B)  frack^22

(C)  (k)/(2√(x))

(D)  2k²

5.  A piecewise motion v(t) profile consists of acceleration from 0 to V_(max) at rate a, constant velocity V_(max) for interval T₀, and deceleration to rest at rate b. If total distance is S, total elapsed time is:

(A)  (S)/(V_max) + fracV_max2( (1)/(a) + (1)/(b) )

(B)  (S)/(V_max) + fracV_max2( (1)/(a) – (1)/(b) )

(C)  (S)/(V_max) – fracV_max2( (1)/(a) + (1)/(b) )

(D)  (2S)/(V_max) + ( (1)/(a) + (1)/(b) )

6.  In a system of blocks A and B connected via an ideal inextensible string over a pulley, the displacement constraint equation is 2y_(A) + 3y_(B) = constant. If block A moves downward with acceleration a_(A) = 4 m/s², block B accelerates upward at:

(A)  2.67 m/s²

(B)  6.00 m/s²

(C)  1.33 m/s²

(D)  8.00 m/s²

7.  Two blocks A and B rest on a horizontal surface connected by a string. A movable pulley P is pulled horizontally with force F. Using virtual work sum_^T cdot v = 0, if velocity of pulley is u, the relation between velocities v_(A) and v_(B) (assuming string segments stay parallel) satisfies v_(A) + v_(B)=:

(A)  u

(B)  2u

(C)  (u)/(2)

(D)  4u

8.  A wedge of angle θ slides leftward on a horizontal table with velocity u. A block resting on its inclined face slides downward relative to the incline with relative speed v_(r). The horizontal component of absolute velocity of the block is:

(A)  v_(r)cos θ − u

(B)  u − v_(r)cos θ

(C)  u + v_(r)cos θ

(D)  v_(r)sin θ + u

9.  A projectile launched with speed u at angle θ above horizontal has radius of curvature at its apex equal to:

(A)  fracu^2cos^2θg

(B)  fracu^2sin^2θg

(C)  fracu^2gcosθ

(D)  fracu^2g

10.  A particle is thrown with speed u = 20 m/s at 60° to horizontal. The time when its velocity vector makes an angle of 45° with horizontal during descent is (g = 10 m/s²):

(A)  1 + √(3)~s

(B)  √(3) – 1~s

(C)  2√(3)~s

(D)  (√(3) + 1)/(2)~s

11.  A body moves along a space path r(t) = 2t²i + (t³−4t)j + 5k m. Frame S’ translates relative to S with r_(O’/O)(t) = t²i + 2tj. The position vector r'(2 s) in Frame S’ is:

(A)  4i + 4j + 5k m

(B)  4i − 4j + 5k m

(C)  8i + 0j + 5k m

(D)  4i + 0j + 5k m

12.  Path length S covered by a particle executing circular motion of radius R = 5 m varies with time as S(t) = 2t² m. Magnitude of total acceleration at t = 1 s is:

(A)  4 m/s²

(B)  3.2 m/s²

(C)  √(16 + 10.24)~m/s^2 approx 5.12~m/s^2

(D)  8 m/s²

13.  Particle 1 is projected vertically upward from top of a tower of height H with speed u. Simultaneously, Particle 2 is dropped from rest from the same point. Relative acceleration a_(1/2) during flight before either hits ground is:

(A)  g downward

(B)  2g downward

(C)  Zero

(D)  g upward

14.  A car moves at uniform speed v₀ = 25 m/s. Driver sees an obstacle and applies brakes after reaction time t_(r) = 0.4 s, producing uniform deceleration a = 5 m/s². Total stopping distance is:

(A)  62.5 m

(B)  72.5 m

(C)  82.5 m

(D)  100 m

15.  Two particles A and B are separated by distance L on a line. They move toward each other with constant speeds v_(A) and v_(B). Time taken to collide is:

(A)  (L)/(v_A) – v_B

(B)  (L)/(v_A) + v_B

(C)  (2L)/(v_A) + v_B

(D)  (L)/(√(v_A)^2) + v_B^2

16.  Motion of a particle along x-axis is governed by a(v) = − αv² where α > 0 is a constant. If initial velocity at x = 0 is v₀, velocity as a function of position x is:

(A)  v(x) = v₀e^(−αx)

(B)  v(x) = v₀ − αx

(C)  v(x) = fracv_01 + α v_0x

(D)  v(x) = √(v_0)^2 – 2α x

17.  Velocity-time profile of a body is triangular: v(t) increases linearly from 0 to V₀ in interval 0 ≤ t ≤ T, then decreases linearly from V₀ to 0 in interval T < t ≤ 3T. Ratio of distance covered in second stage to first stage is:

(A)  1 : 1

(B)  2 : 1

(C)  3 : 1

(D)  4 : 1

18.  Acceleration profile a(t) = a₀sin (ωt) with initial conditions x(0) = 0, v(0) = 0. Maximum velocity reached during first half cycle is:

(A)  fraca_0ω

(B)  frac2a_0ω

(C)  fraca_02ω

(D)  a₀ω

19.  A particle moves piecewise with speed v₁ for time t₁, v₂ for time t₂, and v₃ for time t₃. Average speed over total duration is:

(A)  fracv_1 + v_2 + v_33

(B)  fracv_1t_1 + v_2t_2 + v_3t_3t_1 + t_2 + t_3

(C)  fract_1 + t_2 + t_3fract_1v_1 + fract_2v_2 + fract_3v_3

(D)  √(fracv_1)^2t_1 + v_2^2t_2 + v_3^2t_3t_1 + t_2 + t_3

20.  A system consists of a block A on a horizontal plane connected by string segment 1 to a pulley, which is connected by string segment 2 over a fixed pulley to block B. The geometric constraint gives x_(A) + 2y_(B) = L. If v_(B) = 3 m/s downward, v_(A) is:

(A)  1.5 m/s left

(B)  3.0 m/s left

(C)  6.0 m/s left

(D)  12.0 m/s left

21.  Block A rests on top of block B on a smooth plane. A string connected to A passes around a pulley on B and attaches to a fixed wall. If B moves right with speed u, speed of A relative to ground is:

(A)  u

(B)  2u

(C)  (u)/(2)

(D)  Zero

22.  Block B slides down a stationary wedge W of slope θ with acceleration a_(r) relative to wedge face. If wedge W itself is forced to accelerate horizontally rightward with acceleration A₀, absolute vertical acceleration component of block B is:

(A)  a_(r)sin θ

(B)  a_(r)sin θ + A₀cos θ

(C)  a_(r)cos θ − A₀sin θ

(D)  A₀tan θ

23.  A particle is projected from origin with speed u at angle θ. Equation of trajectory is y = √(3)x – fracgx^220. Initial angle of projection θ is:

(A)  30°

(B)  45°

(C)  60°

(D)  75°

24.  Range R of a projectile launched on level ground is 160 m and time of flight T = 4 s. Horizontal component of initial velocity is (g = 10 m/s²):

(A)  20 m/s

(B)  40 m/s

(C)  50 m/s

(D)  80 m/s

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.