Question

A car is travelling on a straight level road with a speed of 60 km/hr is followed by another car B which is moving with a speed of 70 km/hr.When the distance between them is 2.5 km,The B car is given an accelaration of 20km/hr.After what distance and time will the car B catch up with car A?​
(answer is 32.5km and 0.5h)

Answer 1

Answer:

Explanation:

car-A travels at a speed of 60 km/hr. car-B travels at a speed of 70 km/hr. Let us consider car-B travelling ahead and the distance between car-A and car-B is 2.5 km when car-B started decelerating at 20 km/(hr)2. Let, after travelling X km in t hours, car-B catches up car-A. We can write the equation of motion as follows.

 

for car-A : X = 70×t - (1/2)×20×t2 ...............(1)

for car-B : 60×t = x+2.5 ......................(2)

by eliminating X in (1) and (2), we get  60×t-2.5 = 70×t-(1/2)×20×t2 ...............(3)

 

Solving for t in (3) we get t = (1+√2)/2 = 1.207 hr and X = 69.92 km