A car moves a distance of $200\ m$. It covers first half of the distance at speed $60\ kmh^{- 1}$ and the second half at speed $v$. If the average speed is $40\ kmh^{- 1}$, the value of $v$ is

Question

Dr. Abubacker · Accepted Answer

(a) Time taken by the car to cover first half of the distance is
$t_{1} = \frac{100}{60}$
Time taken by the car to cover speed half of the distance is
$t_{2} = \frac{100}{v}$
Average speed , $v_{av} = \frac{Total\ distance\ travelled}{TOtal\ time\ taken}$
$v_{av} = \frac{100 + 100}{t_{1} + t_{2}} \Rightarrow 40 = \frac{200}{\frac{100}{60} + \frac{100}{v}}$
$\frac{1}{60} + \frac{1}{v} = \frac{1}{20} \Rightarrow \frac{1}{v} = \frac{1}{20} - \frac{1}{60}$
$\frac{1}{v} = \frac{2}{60} = \frac{1}{30}$
$v = 30km\ h^{- 1}$

Q. A car moves a distance of $200\ m$. It covers first half of the distance at speed $60\ kmh^{- 1}$ and the second half at speed $v$. If the average speed is $40\ kmh^{- 1}$, the value of $v$ is

Explanation

Reviewed by Dr. Abubacker

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