Question

A car is traveling on a straight level road with a speed of 60 km/hr it followed by another car b which is moving with a speed of 70km/hr when the distance between them 2.5 km the car b is given a deceleration of 20km/hr after what distance and time will the car b catch up with car a

Answer 1

Distance covered by car A in time t is, s1 = 60 t For car B: Using the second equation of motion: s = ut + 1 2 12at2 where: s = distance covered = s2 u = initial velocity = 70 km/h a = acceleration = -20 km/h t = time = t s = ut + 1 2 12at2 s2 = 70t + 1 2 12 (-20) × t2 s2 = 70t – 10 t2 But it is given that s2 – s1 =2.5 km 70t – 10 t2 - 60 t = 2.5 10t - 10 t2 = 2.5 t – t2 = 0.25 t – t2 – 0.25 =0 t2 –t +0.25 =0 (t – 0.5)2 =0 t = 0.5 hr