Question

A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s2, and the car has an acceleration of 3.40 m/s2. The car overtakes the truck after the truck has moved 60.0 m. (a) How much time does it take the car to overtake the truck

Answer 1

Time take by car to overtake the truck is 7.6 seconds.

Explanation:

Given : A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s², and the car has an acceleration of 3.40 m/s². The car overtakes the truck after the truck has moved 60.0 m.

To find : How much time does it take the car to overtake the truck ?

Solution :

According to question,

Taking the origin to be the truck position when it is at rest.

The car overtakes the truck after the truck has moved 60.0 m.

Using the equation to find time,

`x-x_o=v_ot+(1)/(2)at^2`

Where,
`x_o=0` initial distance

`v_o=0` initial velocity

a= 2.10 m/s² is the acceleration of the truck

x=60 m is the distance truck moved.

Substitute the value in the formula,

`60-0=0(t)+(1)/(2)* 2.10* t^2`

`60=1.05* t^2`

`t^2=(60)/(1.05)`

`t=\sqrt{(60)/(1.05)}`

`t=7.55`

Therefore, Time take by car to overtake the truck is 7.6 seconds.