Question

13.
A car A is travelling along a straight level road with a uniform speed of 60 km/h. It is followed
by another car B which is travelling uniformly at 70 km/h. When the distance between them is
2.5 km, the car B decelerates at 20 km/h? Where will B catch up with A?
(75 km from starting point)

Answer 1

Answer:

Distance covered by car A in time t is, s1 = 60 t

For car B:

Using the second equation of motion: s = ut +

at2

where: s = distance covered = s2

u = initial velocity = 70 km/ha = acceleration = -20 km/ht = time = t

s = ut +

at2

s2 = 70t +

(-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