Question

A car A is travelling on a straight level road with a speed of 60km/hr. It is followed by another car B which is moving with a speed of 70km/hr. when the distance between them is 2.5km, the car B is given a deceleration of 20 km / hr ^{2}. After what distance will the car B catch up with car A.

Answer 1

Answer:

Suppose car B catches up the car A in t hours.

the distance travelled by car A moving with a velocity of 60kmhr−1 in time t hours is given by, S1=60tkm

For the motion of car B

The distance travelled by the car B moving with an intrial velocity u=70kmhr−1 and decelerated at the rate of 20kmhr−2 in time t hour is given by,

S2=ut+at12at2=70t+12(−20)t2,S2=70t−10t2(or)ButS2−S1=2.5km

∴70t−10t2−60t=2.5

i.e., 10t2−10t+2.5=0or4t2−4t+1=0(or)(2t−l)2=0i.e.,2t−l=0,t=1/2=0.5hr−1

using relative velocity concept,

u=70−60=10kmhr−1,v=60−60=0,a=−20kmhr−1

t=v−ua=0−10−20=0.5hr−1, Since S2=70t−10t2

Putting value of t, we get , S2=70×0.5−10×(0.5)2=35−3.5∴S2=32.5km