Two particles A and B are moving in the same direction on a straight line with velocities 10 m/sand 5 m/s respectively. When A is 20 meters behind B, A starts accelerating at 2 m/s^2. How long will it take for A to overtake B?

B. 4 seconds — Use relative motion. The relative initial velocity is 5 m/sand relative acceleration is 2 m/s^2. Solve the equation s = ut + 0.5at^2 for t.

JEE Main · PhysicsMedium

$Two particles A and B are moving in the same direction on a straight line with velocities v_{A} = 10 m/s and v_{B} = 5 m/s respectively. When A is 20 m behind B, A starts accelerating at a_{A} = 2 m/s^{2} . How long will it take for A to overtake B?$

A. $2 seconds$
B. $4 seconds$
C. $5 seconds$
D. $8 seconds$

Show correct answer & step-by-step solution

Correct answer: B — $4 seconds$

Solution

Relative displacement s_{r e l} = 20 m, relative velocity u_{r e l} = 10 - 5 = 5 m/s, relative acceleration a_{r e l} = 2 m/s^{2} . Using s = u t + 0.5 a t^{2}, we get 20 = 5 t + 0.5 (2) t^{2}, which simplifies to t^{2} + 5 t - 20 = 0 . Solving for t gives t = 4 s .

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Two particles A and B are moving in the same direction on a straight line with velocities vA​=10 m/s and vB​=5 m/s respectively. When A is 20 m behind B, A starts accelerating at aA​=2 m/s2. How long will it take for A to overtake B?

Solution

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More Kinematics practice questions

$Two particles A and B are moving in the same direction on a straight line with velocities v_{A} = 10 m/s and v_{B} = 5 m/s respectively. When A is 20 m behind B, A starts accelerating at a_{A} = 2 m/s^{2} . How long will it take for A to overtake B?$