Car A starts from rest with constant acceleration 4 m s⁻² while car B, initially 10 m ahead, moves in the same direction at constant speed 1 m s⁻¹. Find the time in seconds when A overtakes B.
Physics · Kinematics part-3 Relative motion · Relative motion in one dimension
JEE Mains NEET

Question

Car A starts from rest with constant acceleration 4 m s⁻² while car B, initially 10 m ahead, moves in the same direction at constant speed 1 m s⁻¹. Find the time in seconds when A overtakes B.

G1 Physics · Accepted Answer

Relative to B: Initial relative velocity: uᵣ =0-1=-1 m s⁻¹. Relative acceleration: aᵣ =4-0=4 m s⁻². Relative displacement needed =10 m. Use 10 = uᵣt + (1/2)aᵣt² 10 = -t +2t². So 2t²-t-10=0. The positive root is t = (1+9)/4 =2.5 s.