Question

A delivery truck is 5km away from a car. The two started at the same time and headed towards the same direction. The delivery truck accelerates at 3m/s^2. If the car should overtake the truck in ten minutes, what should be the acceleration of the car?

Answer 1

Let's first write the displacements of the car and delivery truck:

$$x_{car}=\dfrac{1}{2}a_{car}t^2,$$ $$x_{truck}=x_0+\dfrac{1}{2}a_{truck}t^2.$$

At the time when the car overtakes the truck, $x_{car}=x_{truck}$:

$$\dfrac{1}{2}a_{car}t^2=x_0+\dfrac{1}{2}a_{truck}t^2,$$ $$a_{car}=\dfrac{2(x_0+\dfrac{1}{2}a_{truck}t^2)}{t^2},$$ $$a_{car}=\dfrac{2\cdot(5000\ m+\dfrac{1}{2}\cdot3\ \dfrac{m}{s^2}\cdot(600\ s)^2)}{(600\ s)^2}=3.03\ \dfrac{m}{s^2}.$$