A car accelerates at a constant rate from zero to 32.6 m/s in 10 seconds and then slows to 14.8 m/s in 5 seconds. What is its average acceleration to the nearest tenth of a m/s2 during the 15 seconds?
What was the acceleration during the first 10 seconds in the previous problem?
The average acceleration is the net velocity change divided by the time interval. For your first question, that would be 14.8 m/s divided by 15 s, which rounds off to 1.0 m/s^2.
For your second question, the answer is 32.6 m/s divided by 10 s.
To find the average acceleration during the 15 seconds, we need to calculate the total change in velocity and divide it by the total time.
First, let's calculate the change in velocity in the first 10 seconds:
Final velocity = 32.6 m/s
Initial velocity = 0 m/s
Change in velocity = Final velocity - Initial velocity
Change in velocity = 32.6 m/s - 0 m/s
Change in velocity = 32.6 m/s
Next, let's calculate the change in velocity in the last 5 seconds:
Final velocity = 14.8 m/s
Initial velocity = 32.6 m/s
Change in velocity = Final velocity - Initial velocity
Change in velocity = 14.8 m/s - 32.6 m/s
Change in velocity = -17.8 m/s
Now, let's calculate the average acceleration:
Total change in velocity = Change in velocity (first 10 seconds) + Change in velocity (last 5 seconds)
Total change in velocity = 32.6 m/s + (-17.8 m/s)
Total change in velocity = 14.8 m/s
Total time = 15 seconds
Average acceleration = Total change in velocity / Total time
Average acceleration = 14.8 m/s / 15 s
Average acceleration ≈ 0.99 m/s^2 (rounded to the nearest tenth)
Therefore, the average acceleration during the 15 seconds is approximately 0.99 m/s^2.
To find the acceleration during the first 10 seconds, we can use the change in velocity and the given time interval.
Acceleration = Change in velocity / Time interval
Acceleration = 32.6 m/s / 10 s
Acceleration = 3.26 m/s^2
Therefore, the acceleration during the first 10 seconds is 3.26 m/s^2.
To find the average acceleration during the 15 seconds, we need to find the total change in velocity and divide it by the total change in time.
The total change in velocity can be calculated by subtracting the initial velocity from the final velocity. In the first 10 seconds, the car accelerates from zero to 32.6 m/s, so the change in velocity is 32.6 m/s - 0 m/s = 32.6 m/s.
The total change in time is the sum of the time it took to accelerate and the time it took to decelerate, which is 10 seconds + 5 seconds = 15 seconds.
Now we can calculate the average acceleration:
Average acceleration = (change in velocity) / (change in time)
= 32.6 m/s / 15 s
≈ 2.17 m/s^2
Therefore, the average acceleration of the car during the 15 seconds is approximately 2.17 m/s^2.
To find the acceleration during the first 10 seconds in the previous problem, we can use the formula for average acceleration:
Average acceleration = (change in velocity) / (change in time)
= 32.6 m/s / 10 s
= 3.26 m/s^2
Therefore, the acceleration during the first 10 seconds in the previous problem is 3.26 m/s^2.