a car accelerates at a constant rate from zero to 26.7 m/s in 10 seconds and then slows to 19 m/s in 5 seconds. What is its average acceleration to the nearest tenth of a m/s^2 during the 15 seconds?

Avg. acceleration = (Velocity change)/time

= 19/15 = 1.27
-> 1.3 m/s^2 (rounding to nearest tenth)

Only the initial and final velocity matter when you want the average acceleration

To find the average acceleration during the given time interval, you need to calculate the overall change in velocity and divide it by the total time.

First, let's find the change in velocity during the first 10 seconds. The car accelerates from 0 m/s to 26.7 m/s, so the change in velocity is 26.7 m/s - 0 m/s = 26.7 m/s.

Next, let's find the change in velocity during the next 5 seconds. The car slows down from 26.7 m/s to 19 m/s, so the change in velocity is 19 m/s - 26.7 m/s = -7.7 m/s. Note that the negative sign indicates deceleration.

Now, let's calculate the total change in velocity. Adding the changes in velocity during the acceleration and deceleration phases: 26.7 m/s + (-7.7 m/s) = 19 m/s.

Finally, we'll calculate the average acceleration by dividing the total change in velocity by the total time. The total time in this case is 15 seconds (10 seconds of acceleration + 5 seconds of deceleration).

Average acceleration = total change in velocity / total time
Average acceleration = 19 m/s / 15 s ≈ 1.3 m/s^2 (rounded to the nearest tenth)

Therefore, the car's average acceleration during the 15 seconds is approximately 1.3 m/s^2.