A car accelerates at a constant rate from zero to 25.6 m/s in 10 seconds and then slows to 14.4 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?
To find the average acceleration over the 15 seconds, we need to calculate the change in velocity and divide it by the total time.
1. Calculate the change in velocity: The car accelerates from 0 to 25.6 m/s and then slows down to 14.4 m/s. The change in velocity during acceleration is 25.6 m/s - 0 m/s = 25.6 m/s. The change in velocity during deceleration is 14.4 m/s - 25.6 m/s = -11.2 m/s.
2. Calculate the total time: The car accelerates for 10 seconds and then decelerates for 5 seconds. The total time is 10 seconds + 5 seconds = 15 seconds.
3. Calculate the average acceleration: Average acceleration = (change in velocity) / (total time)
Average acceleration = (25.6 m/s + (-11.2 m/s)) / 15 seconds
Average acceleration = 14.4 m/s / 15 seconds
Rounding to one decimal place, the average acceleration during the 15 seconds is approximately 0.96 m/s².
4. Calculate the acceleration during the first 10 seconds: The acceleration during the first 10 seconds is the same as the average acceleration, which is approximately 0.96 m/s².
To find the average acceleration of the car during the 15 seconds, we can use the formula:
Average acceleration = (change in velocity) / (time taken)
First, let's calculate the change in velocity during the 15 seconds. The car accelerates from 0 m/s to 25.6 m/s in the first 10 seconds, and then it slows down from 25.6 m/s to 14.4 m/s in the next 5 seconds.
Change in velocity = final velocity - initial velocity
In the first 10 seconds:
Initial velocity = 0 m/s
Final velocity = 25.6 m/s
Change in velocity = 25.6 m/s - 0 m/s = 25.6 m/s
In the next 5 seconds:
Initial velocity = 25.6 m/s
Final velocity = 14.4 m/s
Change in velocity = 14.4 m/s - 25.6 m/s = -11.2 m/s (negative because it's slowing down)
Now, let's calculate the average acceleration during the 15 seconds:
Average acceleration = (change in velocity) / (time taken)
For the 15 seconds, the total time taken is 15 seconds.
Average acceleration = (25.6 m/s - 11.2 m/s) / 15 s ≈ 0.93 m/s²
So, the average acceleration of the car during the 15 seconds is approximately 0.93 m/s², rounded to the nearest tenth of a m/s².
To find the acceleration during the first 10 seconds, we use the same formula:
Acceleration = (change in velocity) / (time taken)
During the first 10 seconds, the change in velocity is 25.6 m/s - 0 m/s = 25.6 m/s.
Acceleration = 25.6 m/s / 10 s = 2.56 m/s²
So, the acceleration during the first 10 seconds is 2.56 m/s², rounded to the nearest tenth of a m/s².