Question

At the instant a traffic light turns green, a car starts with a constant acceleration of 1.3 m/s2. At the same instant a truck, traveling with a constant speed of 7.0 m/s, overtakes and passes the car.
(a)How far beyond the traffic signal will the car overtake the truck?
(b)What will the velocity of the car be at that instant?

Answer 1

Answer:

(a) Distance traveled = 75.3846 m

(b) Velocity of car at that instant will be 14 m/sec

Explanation:

We have given acceleration of the car $a=1.3m/sec^2$

Initial velocity of the cart u = 0 m/sec

(a) According to second equation of motion we know that $s=ut+\frac{1}{2}at^2$

So distance traveled by car $s_c=0\times t+\frac{1}{2}\times 1.3t^2=0.65t^2$

As the truck is moving with constant speed

So distance traveled by truck $s_t=ut=7t$

As the truck overtakes the car

So $s_c=s_t$

$0.65t^2=7t$

$t=10.769sec$

So distance traveled $s_c=s_t=7\times 10.769=75.3846m$

(b) From second equation of motion we know that v = u+at

So v = 0+1.3×10.769 = 14 m /sec