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Time and Speed

A body moves ...

Question

A body moves at a speed of 100 $m s^{- 1}$ for 10 s and then moves at a speed of 200 $m s^{- 1}$ for 20 s along the same direction. The average speed is ______.

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Solution

Given
$u_{1} = 100 m / s$ $t_{1} = 10 s$
$u_{1} = 200 m / s$ $t_{1} = 20 s$

Average speed= $\frac{Total Distance}{Total Time} = \frac{u_{1} \times t_{1} + u_{2} \times t_{2}}{t_{1} + t_{2}} = \frac{100 \times 10 + 200 \times 20}{10 + 20}$
$S_{a v g} = \frac{100 + 400}{30} = \frac{500}{30} = \frac{50}{3} m / s$

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