If Jill starts out at 20 m/s, and in 10 seconds speeds up to 40 m/s, what is her acceleration?

Saturday, June 21, 2014

If Jill starts out at 20 m/s, and in 10 seconds speeds up to 40 m/s, what is her acceleration?

Hello!

The acceleration is probably considered constant (uniform). Denote it as $\displaystyle{a}{\left(\frac{{m}}{{{s}}^{{2}}}\right)}.$

Then during each second Jill's speed $\displaystyle{V}$ becomes more by $\displaystyle{a}\frac{{m}}{{s}}.$ Therefore for any time $\displaystyle{t}$ after the start the speed is $\displaystyle{V}{\left({t}\right)}={V}_{{0}}+{a}{t},$ where $\displaystyle{V}_{{0}}={20}\frac{{m}}{{s}}$ is the initial speed.

It is given that for the final moment $\displaystyle{t}_{{1}}={10}{s}$ the speed is $\displaystyle{V}_{{1}}={40}\frac{{m}}{{s}}.$ Therefore $\displaystyle{V}_{{1}}={V}{\left({t}_{{1}}\right)}={V}_{{0}}+{a}{t}_{{1}},$ and we can easily find $\displaystyle{a}=\frac{{{V}_{{1}}-{V}_{{0}}}}{{t}_{{1}}}.$

In numbers it is equal to $\displaystyle\frac{{{40}-{20}}}{{10}}={2}{\left(\frac{{m}}{{{s}}^{{2}}}\right)}.$ This is the answer.

That said, $\displaystyle{40}\frac{{m}}{{s}}$ and even $\displaystyle{20}\frac{{m}}{{s}}$ is too high speed for running, probably Jill used some equipment, for example a bicycle. Also note that the same speeds could be reached within non-constant acceleration, but there are infinitely many non-constant functions $\displaystyle{a}{\left({t}\right)}$ which satisfy the given conditions.

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Saturday, June 21, 2014