Question

At a stop light, a truck traveling at 10.5 m/s passes a car as it starts from rest. The truck travels at constant velocity and the car accelerates at 3 m/s2. How much time does the car take to catch up to the truck?

Answer 1

t = 7 sec.

Step-by-step explanation:

As the car and the truck travel the same distance, assuming a constant acceleration, we can describe the movement of the truck and the car with these equations for this same displacement:

x(truck) = v*t (1)

x(car) =
`(1)/(2)*a*t^(2) (2)`

As the left sides of (1) and (2) are equal each other, the same must be true for the right sides:

v*t =
`(1)/(2)*a*t^(2)`

Solving for t, replacing v= 10.5 m/s and a= 3 m/s², we have:

`t = (2*v)/(a) = (2*10.5 m/s)/(3 m/s2) = 7 sec.`

⇒ t = 7 sec.