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?
3.028m/s^2
To solve this problem, we need to determine the acceleration of the car. Let's break down the information given:
1. The delivery truck and car both start at the same time and head in the same direction.
2. The delivery truck has an acceleration of 3 m/s^2.
3. The car overtakes the truck in 10 minutes.
First, let's convert the time from minutes to seconds, as the unit of acceleration is also in seconds:
10 minutes = 10 * 60 seconds = 600 seconds
Now, let's calculate the distance covered by the truck and car in these 600 seconds.
The distance covered by an object can be calculated using the formula:
Distance = Initial velocity * time + (0.5 * acceleration * time^2)
For the delivery truck:
Initial velocity of the truck = 0 m/s (since it starts from rest)
Time = 600 seconds
Acceleration of the truck = 3 m/s^2
Using the formula:
Distance_truck = 0 * 600 + (0.5 * 3 * (600)^2)
Now, let's calculate the distance covered by the car, which overtakes the truck.
The car covers the same distance as the truck, so:
Distance_car = Distance_truck
Now, use the formula for the distance covered by the car, assuming it has an acceleration of "a" m/s^2:
Distance_car = 0 * 600 + (0.5 * a * (600)^2)
Since the truck and car cover the same distance, we can equate the two expressions:
0 * 600 + (0.5 * 3 * (600)^2) = 0 * 600 + (0.5 * a * (600)^2)
After simplifying the equation:
3 * 360000 = a * 360000
Divide both sides of the equation by 360000:
3 = a
Therefore, the acceleration of the car should be 3 m/s^2 to overtake the delivery truck in 10 minutes.