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

Answer:

t = 7 sec.

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) = $\frac{1}{2}*a*t^{2} (2)$

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

v*t = $\frac{1}{2}*a*t^{2}$

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

$t = \frac{2*v}{a} = \frac{2*10.5 m/s}{3 m/s2} = 7 sec.$

⇒ t = 7 sec.