Question

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.70 m/s2. At the same instant a truck, traveling with a constant speed of 9.50 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck

Answer 1

66.85 m

Step-by-step explanation:

We are given that

Acceleration ,a=
`2.7m/s^2`

Speed of truck, v=9.5 m/s

We have to find the distance beyond which the traffic signal will the automobile overtake the truck.

Initial speed of automobile, u=0

We know that

`s=ut+(1)/(2)at^2`

Using the formula

`s=0+(1)/(2)(27)t^2=(27)/(2)t^2`

For constant speed

Acceleration, a=0

Again

`s=vt+0=9.5t`

`9.5t=(27)/(2)t^2`

`t=(9.5* 2)/(2.7)=7.037s`

Substitute the value of t

`x=9.5(7.037)=66.85m`

Hence, the distance beyond which the traffic signal will the automobile overtake the truck=66.85 m