A bank robber in a getaway car approaches an intersection at a speed of 45 mph. Just as he passes the intersection, he realizes that he needed to turn. So he steps on the brakes, comes to a complete stop, and then accelerates driving straight backward. He reaches a speed of 22.5 mph moving backward. Altogether his deceleration and reacceleration in the opposite direction take 12.4 s. What is the average acceleration during this time?
To find the average acceleration, we need to use the formula:
average acceleration = change in velocity / time taken
First, let's find the change in velocity. The robber's initial velocity was 45 mph, and then he accelerated to 22.5 mph in the opposite direction. Therefore, the change in velocity is:
change in velocity = final velocity - initial velocity
change in velocity = 22.5 mph - (-45 mph)
change in velocity = 22.5 mph + 45 mph
change in velocity = 67.5 mph
Next, we need to find the time taken for both deceleration and reacceleration. According to the given information, the total time taken is 12.4 seconds.
Now we can calculate the average acceleration:
average acceleration = change in velocity / time taken
average acceleration = 67.5 mph / 12.4 s
To convert mph to m/s, we multiply by a conversion factor: 1 mph = 0.44704 m/s.
average acceleration = (67.5 mph * 0.44704 m/s) / 12.4 s
average acceleration = 30.1492 m/s / 12.4 s
average acceleration ≈ 2.43 m/s²
Therefore, the average acceleration during the deceleration and reacceleration is approximately 2.43 m/s².