An object moving on a straight line covers first half of the dist… - Vidyadip

Question

An object moving on a straight line covers first half of the distance at speed $v$ and second half of the distance at speed $2v.$ Find:

Aaverage speed.
Mean speed.

✓

Answer

Let total distance be $x.$
Distance of first half $=\frac{\text{x}}{2},$ Speed $= v$
Time taken $t_1=\frac{\frac{\text{x}}{2}}{\text{v}}=\frac{\text{x}}{2\text{v}}$
Distance of second half $=\frac{\text{x}}{2},$
Speed $= 2v$
Time taken $t_2$ $=\frac{\frac{\text{x}}{2}}{2\text{v}}=\frac{\text{x}}{4\text{v}}$

Average speed $=\frac{\text{Total distance travelled}}{\text{Total time taken}}$

$=\frac{\text{x}}{\frac{\text{x}}{2\text{v}}+\frac{\text{x}}{4\text{v}}}=\frac{4\text{v}}{3}$

Mean speed $=\frac{\text{v}+2\text{v}}{2}=\frac{3\text{v}}{2}$

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