A delivery van drives the first 24 km of a straight road at 48 km/h, and the next 24 km at 32 km/h…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A delivery van drives the first $24\ \text{km}$ of a straight road at $48\ \text{km/h}$ , and the next $24\ \text{km}$ at $32\ \text{km/h}$ in heavy traffic.

What is its average speed for the $48\ \text{km}$ ?
The driver wants an average of $40\ \text{km/h}$ . Keeping the first half the same, how fast must the second half be?

Need a reminder? The key ideaShow

Over a time $\Delta t$ :

\displaystyle \text{average speed} = \frac{\text{path length}}{\Delta t}

\displaystyle v_{\text{av}} = \frac{\Delta x}{\Delta t}

Average speed is never negative; average velocity has the sign of the displacement.

For two equal distances at speeds $v_1$ and $v_2$ , the average speed is $\dfrac{2v_1v_2}{v_1 + v_2}$ , never the simple mean.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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