A runner, beginning from x = 0 and t = 0, accelerates at a constant rate for 10 seconds and reaches a speed of 8 m/sec. The runner maintains that speed  until he reaches x = 100 m. Find t100, the time at which the runner reaches 100 m. Explain your approach and assumptions.

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Asked Nov 24, 2019
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A runner, beginning from x = 0 and t = 0, accelerates at a constant rate for 10 seconds and reaches a speed of 8 m/sec. The runner maintains that speed  until he reaches x = 100 m. Find t100, the time at which the runner reaches 100 m. Explain your approach and assumptions.

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Expert Answer

Step 1

Write the expression of the velocity as a function of time.

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v=1 + at v-0 a=- t 8 m/s 0 m/s a = 10 s a 0.8 m/s

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Step 2

At this acceleration the runner travels for 10 seconds. Therefore, the distance travelled in the 10 seconds is:

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1 2 S 00.8 m/s(10 s) s 40 m

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Step 3

Remaining distance that the runner tra...

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Remaining distance (d') = 100 m-40 m = 60 m

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