A car accelerates at a constant rate from zero to 20.5 m/s in 10 seconds and then slows to 15.9 m/s in 5 seconds. What is its average acceleration to the nearest tenth of a m/s2 during the 15 seconds?
The average acceleration during a period of time is the start-to-finish velocity change, divided by the length of time.
In this case, that would be
(15.9 m/s)/15 s = 1.06 m/s^2
To find the average acceleration of the car, we can use the formula:
Average acceleration = (change in velocity) / (time taken)
Let's calculate the change in velocity during the first 10 seconds:
Change in velocity = Final velocity - Initial velocity = 20.5 m/s - 0 m/s = 20.5 m/s
Now, let's calculate the change in velocity during the next 5 seconds:
Change in velocity = Final velocity - Initial velocity = 15.9 m/s - 20.5 m/s = -4.6 m/s
Note that since the car is slowing down, the change in velocity is negative.
Next, we'll calculate the total change in velocity during the 15 seconds by adding the two changes in velocity:
Total change in velocity = 20.5 m/s + (-4.6 m/s) = 15.9 m/s
Now, let's calculate the average acceleration:
Average acceleration = Total change in velocity / Total time taken = 15.9 m/s / 15 s = 1.06 m/s^2
Therefore, the average acceleration of the car during the 15 seconds is approximately 1.1 m/s^2 (rounded to the nearest tenth).
To calculate the average acceleration, we need to determine the change in velocity and the corresponding change in time.
1. Calculate the change in velocity:
The car accelerates from zero to 20.5 m/s in the first 10 seconds. Therefore, the change in velocity during this period is 20.5 m/s - 0 m/s = 20.5 m/s.
Then, the car slows down from 20.5 m/s to 15.9 m/s in the next 5 seconds. Hence, the change in velocity during this period is 15.9 m/s - 20.5 m/s = -4.6 m/s. Note that the negative sign indicates a decrease in velocity.
2. Calculate the change in time:
The total time taken is the sum of the acceleration time and the deceleration time. Therefore, the change in time is 10 seconds + 5 seconds = 15 seconds.
3. Calculate average acceleration:
Average acceleration is defined as the change in velocity divided by the change in time. So, we divide the total change in velocity by the total change in time.
Average acceleration = (Total change in velocity) / (Total change in time)
Average acceleration = (20.5 m/s + (-4.6 m/s)) / 15 s
Calculating the value, we find:
Average acceleration ≈ 1.27 m/s^2 (rounded to the nearest tenth)
Thus, the average acceleration of the car during the 15 seconds is approximately 1.27 m/s^2.