To find the acceleration of the car, we can use the equation of motion that relates distance, time, initial velocity, and acceleration. We know that the delivery truck is 5 km away from the car, but we will convert this distance to meters for consistency with the units of acceleration.
Given:
Initial distance between the delivery truck and the car = 5 km = 5000 m
Acceleration of the delivery truck = 3 m/s^2
Time taken for the car to overtake the truck = 10 minutes = 10 minutes * 60 seconds/minute = 600 seconds
To find the final distance traveled by the delivery truck, we can use the equation of motion:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Since the delivery truck starts from rest (initial velocity = 0 m/s), the equation simplifies to:
Distance = (1/2) * Acceleration * Time^2
Substituting the given values into the equation:
5000 m = (1/2) * (3 m/s^2) * (600 s)^2
Simplifying the equation:
5000 m = 0.5 * 3 * 360000 s^2
5000 m = 540000 s^2
Dividing both sides by 540000 s^2:
5000 m / 540000 s^2 = 1
Thus, the acceleration of the car should be 1 m/s^2 in order to overtake the delivery truck in ten minutes.