A body travels with velocity $v_{1}$ for time $t_{1}$ second and with velocity $v_{2}$ for time $t_{2}$ second in the same direction. Calculate the average velocity of the body.

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Solution

Step 1:Given data:
The velocity of the body is $v_{1}$ for time $t_{1}$ second.
The velocity of the body is $v_{2}$ for time $t_{2}$ second.
Step 2:Finding total distance traveled by the body:
We know,
$D i s \tan c e = v e l o c i t y \times t i m e .$
Initially,
Distance traveled by the body for time $t_{1}$ is $S_{1} = v_{1} t_{1} .$
Finally,
Distance traveled by the body for time $t_{2}$ is $S_{2} = v_{2} t_{2} .$
Step 3:Finding the average velocity:
Let, $v_{a v g}$ be the average velocity of the body.
Again we know,
$A v e r a g e v e l o c i t y = \frac{T o t a l d i s \tan c e}{T o t a l t i m e} = \frac{S_{1} + S_{2}}{t_{1} + t_{2}} . o r v_{a v g} = \frac{v_{1} t_{1} + v_{2} t_{2}}{t_{1} + t_{2}} .$
Therefore, the average velocity of the body is $v_{a v g} = \frac{v_{1} t_{1} + v_{2} t_{2}}{t_{1} + t_{2}} .$

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