Question

a student releases a marble from the top of a 160cm long ramp. the marble increases speed steadily and reaches the bottom of the ramp with a speed of 120cm/s. determine all unknowns and answer the following question. how long did the marble take to reach the bottom of the ramp?

Explanation:

Step1: Find the average speed

Since the marble increases speed steadily (constant acceleration), the average speed \(v_{avg}\) is given by the formula \(v_{avg}=\frac{v_{i} + v_{f}}{2}\). The initial speed \(v_{i} = 0\) (released from rest), and the final speed \(v_{f}=120\space cm/s\). So, \(v_{avg}=\frac{0 + 120}{2}=60\space cm/s\).

Step2: Calculate the time

We know that the formula for speed is \(v=\frac{d}{t}\), where \(d\) is the distance and \(t\) is the time. Rearranging for \(t\), we get \(t=\frac{d}{v}\). The distance \(d = 160\space cm\) and the average speed \(v = 60\space cm/s\). So, \(t=\frac{160}{60}=\frac{8}{3}\approx2.67\space s\)

Answer:

The marble took approximately \(2.67\space s\) to reach the bottom of the ramp.