a delivery truck is 5 km away from a car. the two started at the same time and headed at the same direction. the delivery truck accelerates at 3m/s. if the car should overtake the truck in ten minutes, what should be the acceleration of the car?
3 m/s is not an acceleration rate. Recheck the wording of the question.
okay lets change that to 3 m/(s^2). how can we solve this.
To find the acceleration of the car, we need to determine the relative speed between the delivery truck and the car.
Given that the delivery truck has an acceleration of 3 m/s and the car overtakes the truck in 10 minutes, we first need to convert the time to seconds.
10 minutes = 10 x 60 = 600 seconds.
Next, we consider the distance traveled by the delivery truck in 600 seconds. Since it has an acceleration of 3 m/s, we can use the formula:
Distance = (initial velocity x time) + (0.5 x acceleration x time squared)
The initial velocity of the delivery truck is zero since it starts from rest.
Distance = (0 x 600) + (0.5 x 3 x 600^2)
= 0 + (0.5 x 3 x 360000)
= 0 + 540000
= 540000 m
Now, we know that the delivery truck is 5 km (or 5000 m) away from the car initially. So, to find the relative distance that the car must travel to overtake the truck, we subtract the initial distance of the truck from the distance to be covered.
Relative distance = 5000 m - 540000 m
= -535000 m
Since the relative distance is negative, it means the car needs to travel 535,000 meters in the same direction as the delivery truck to overtake it.
Now, we can determine the acceleration of the car using the formula:
Distance = (initial velocity x time) + (0.5 x acceleration x time squared)
Since the car starts from rest, its initial velocity is also zero.
-535000 = (0 x t) + (0.5 x acceleration x t^2)
-535000 = (0.5 x acceleration x t^2)
We know that the time taken is 600 seconds.
-535000 = (0.5 x acceleration x 600^2)
Simplifying further:
-535000 = (0.5 x 360000 x acceleration)
-535000 = 180000 x acceleration
acceleration = -535000 / 180000
acceleration = -2.972 m/s^2
Therefore, the acceleration of the car should be approximately -2.972 m/s². The negative sign indicates that the car needs to decelerate in order to overtake the delivery truck.