On one side of the paper solve it using position versus time graphs and on the b

Question

On one side of the paper solve it using position versus time graphs and on the back side solve it with velocity versus time graphs. You will be graded on your ability to communicate a solution using the graphs. PJ can run at a speed of 1.80 m/s, while you can run at 2.50 m/s. Not being as young as a two-year-old, you tire of the running and decide to take a rest. But PJ is not done. He runs by you and 16.0 seconds later you notice he isn’t stopping and is running straight for a busy road. Despite your pleas for him to stop he keeps running. How long will it take you to catch him and how far will you need to run?

Explanation / Answer

This is a problem of relative velocity.

My velocity relative to PJ's velocity = 2.50 m/s - 1.80 m/s = 0.70 m/s

Distance travelled by PJ in 16.0 seconds, d = 1.80 x 16.0 = 28.8 m

(a) So, time taken by me to cover this distance = d / relative velocity = 28.8 / 0.70 = 41.14 s

(b) And I will need to run a distance in the process of catching PJ = 2.50*41.14 = 102.85 meter.

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