Question

# A boy swims in a 90 m long pool. He covers 180 m in one minute by swimming from one end to the other and back along the same straight path. Find the average speed and average velocity of the boy

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Solution

## Step 1: Given dataThe displacement of the boy is zero because after he travels he returns to his initial point of the journey, i.e, $D=0.$The length of the pool is $L=90m.$He travels $180m$ in 1 minute.Time of travelling, $t=60sec.$Average speed and average velocitySpeed is the time rate of change in distance traveled by a body. it is a scalar quantity (has only magnitude ).$averagespeed=\frac{totaldis\mathrm{tan}cetraveledbyabody}{totaltimetaken}$.Velocity is the time rate of change in displacement traveled by a body. It is a vector quantity (has both magnitude and direction).$averagevelocity=\frac{totaldisplacementbyabody}{totaltimetaken}$Step 2: Find the average speedLet ${V}_{s}$ be the average speed of the body.Now, ${V}_{s}$$=\frac{totaldis\mathrm{tan}cetraveledbyabody}{totaltimetaken}=\frac{180m}{\left(1×60\right)sec}=3m/s.$$or{V}_{s}=3m/s$Step 3: Find the average velocityLet ${V}_{v}$ be the average velocity of the body.now,${V}_{v}=\frac{totaldisplacementbyabody}{totaltimetaken}=\frac{0m}{\left(1×60\right)sec}=0\phantom{\rule{0ex}{0ex}}or{V}_{v}=0.$So, the average speed of the body is $3m/s$ and the average velocity of the body is zero.

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