A car accelerates at a constant rate from zero to 28.7 m/s in 10 seconds and then slows to 17.5 m/s in 5 seconds. What is its average acceleration to the nearest tenth of a m/s2 during the 15 seconds?
car changes from 0m/s to 17.5m/s in 15 sec.
Looks like an average acceleration of 17.5m/s / 15s = 1.1666 m/s^2
It doesn't matter how long it did what. The average acceleration only takes into account change in speed and time elapsed.
To find the average acceleration, we need to calculate the total change in velocity and divide it by the total change in time.
First, let's calculate the change in velocity during the first 10 seconds when the car accelerates from zero to 28.7 m/s. The initial velocity is zero, and the final velocity is 28.7 m/s. So, the change in velocity is:
Change in velocity = Final velocity - Initial velocity
Change in velocity = 28.7 m/s - 0 m/s
Change in velocity = 28.7 m/s
Next, let's calculate the change in velocity during the next 5 seconds when the car slows down from 28.7 m/s to 17.5 m/s. The initial velocity is 28.7 m/s, and the final velocity is 17.5 m/s. So, the change in velocity is:
Change in velocity = Final velocity - Initial velocity
Change in velocity = 17.5 m/s - 28.7 m/s
Change in velocity = -11.2 m/s
Note that the change in velocity is negative because the car is slowing down.
Now, let's calculate the total change in velocity during the 15 seconds. We add the change in velocity from the first 10 seconds to the change in velocity from the next 5 seconds:
Total change in velocity = Change in velocity (acceleration period) + Change in velocity (deceleration period)
Total change in velocity = 28.7 m/s + (-11.2 m/s)
Total change in velocity = 17.5 m/s
Finally, we find the average acceleration by dividing the total change in velocity by the total change in time:
Average acceleration = Total change in velocity / Total change in time
Average acceleration = 17.5 m/s / 15 s
Average acceleration = 1.17 m/s² (rounded to the nearest tenth)
Therefore, the average acceleration of the car during the 15 seconds is approximately 1.17 m/s².