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

(a) Distance traveled = 75.3846 m

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

Step-by-step 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+(1)/(2)at^2`

So distance traveled by car
`s_c=0* t+(1)/(2)* 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* 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