Question

Alexander's hobby is dirt biking. on one occasion last weekend, he accelerated from rest to 12.1 m/s in 5.75 seconds. he then maintained this speed for 7.19 seconds. seeing a coyote run cross the trail ahead of him, he abruptly stops in 4.43 seconds. determine alexander's average speed for this motion.

Answer 1

Alexander's average speed for this motion is 17.658 m/s.

Step-by-step explanation:

To determine Alexander's average speed for this motion, we need to calculate the total distance he traveled and the total time it took him.

First, let's calculate the distance he traveled during acceleration. We can use the equation:

d = v0 * t + 0.5 * a * t2

Where v0 is the initial velocity, t is the time, and a is the acceleration.

During acceleration:

d = 0.5 * 0 * (5.75)2 + 0.5 * 4 * (5.75)2 = 0 + 101.5 = 101.5 m

Next, let's calculate the distance during constant speed. Since velocity is constant, the distance is equal to the product of velocity and time:

During constant speed:

d = 12.1 * 7.19 = 87.239 m

Finally, let's calculate the distance during deceleration. Using the same equation as before:

During deceleration:

d = 0.5 * 12.1 * (4.43)2 = 0.5 * 12.1 * 19.6249 = 118.036 m

The total distance traveled is the sum of the distances during acceleration, constant speed, and deceleration:

Total distance = 101.5 + 87.239 + 118.036 = 306.775 m

The total time taken is the sum of the times for acceleration, constant speed, and deceleration:

Total time = 5.75 + 7.19 + 4.43 = 17.37 s

Finally, we can calculate Alexander's average speed using the equation:

Average speed = Total distance / Total time

Average speed = 306.775 m / 17.37 s

Average speed = 17.658 m/s