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?
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.