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You place a small air cart on a 4.00 m air track and set it into motion with a speed of 0.75 m/s. Due to very good elastic bumpers at each end of the track, the cart oscillates back and forth between the two ends of the track with essentially no loss in energy. Determine the period and the frequency for this motion. You may assume that the length of the cart is negligible compared to the length of the track.

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Answer:

6 seconds

0.167 Hz

Explanation:

Distance = 4 m

Velocity = 0.75 m/s

Period is given by

[tex]T=2\times Distance\times Velocity\\\Rightarrow T=2\times 4\times 0.75\\\Rightarrow T=6\ s[/tex]

The period of the motion is 3 seconds

Frequency is given by

[tex]f=\frac{1}{T}\\\Rightarrow f=\frac{1}{6}\\\Rightarrow f=0.167\ Hz[/tex]

The frequency of the motion is 0.33 Hz

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