Question

A pool ball is rolling downhill. It was initially going 0.56 m/s and after precisely 1 23 s. The pool ball was going 2.30 m/s. What distance did the pool cover while rolling?

A) 1.74m
B)2.30m
C)0.56m
D)1.23s

Answer 1

The pool ball covered approximately 1.755245 m, which rounds to 1.74 m. This distance was calculated using the equation of motion for constant acceleration with given initial speed, final speed, and time.

Step-by-step explanation:

The student's question is about calculating the distance that a pool ball covers while rolling downhill when given its initial speed, final speed, and the time it took to change from the initial to the final speed.

To find the distance, we need to use the equation of motion under constant acceleration, which in this case is:

d = v_i * t + ½ * a * t^2

First, we calculate the acceleration:

a = Δv / t = (2.30 m/s - 0.56 m/s) / 1.23 s = 1.41 m/s^2

Now, we can calculate the distance:

d = (0.56 m/s * 1.23 s) + ½ * (1.41 m/s^2 * (1.23 s)^2)

d = 0.6888 m + ½ * 1.41 m/s^2 * 1.5129 s^2

d = 0.6888 m + ½ * 2.13289 m

d = 0.6888 m + 1.066445 m = 1.755245 m

Thus, the approximate distance the pool ball covered while rolling is 1.755245 m, which, when rounded, is closest to option A) 1.74 m.