First slide

Average Velocity

Question

A car is moving along a straight line OP as shown in the figure. It moves from O to P in 18 s and returns from P to Q in 6 s. Which of the following statements is not correct regarding the motion of the car

A : The average speed of the car in going from O to P and come back to Q is 20m $s^{- 1}$
B : The average velocity of the car in going from O to P and come back to Q is 15m $s^{- 1}$

Moderate

A

A,B are true
B

A,B are false
C

A true, B false
D

A false, B true

Solution

$\large Average{\kern 1pt} {\kern 1pt} velocity = \frac{{Displacement}} {{Time{\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} journey}}$
$\large Average{\kern 1pt} {\kern 1pt} speed = \frac{{Length{\kern 1pt} {\kern 1pt} of{\kern 1pt} path{\kern 1pt} {\kern 1pt} {\kern 1pt} traversed}} {{Time{\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} journey}}$
$\large \therefore Average{\kern 1pt} {\kern 1pt} velocity = \frac{{240}} {{18 + 6}}m/s = 10m/s$
$\large \therefore Average{\kern 1pt} {\kern 1pt} {\kern 1pt} speed = \frac{{Length{\kern 1pt} {\kern 1pt} {\kern 1pt} OP + Length{\kern 1pt} {\kern 1pt} {\kern 1pt} PQ}} {{(18 + 6)}}m/s = \frac{{360 + (360 - 240)}} {{24}}m/s \Rightarrow 20m/s$

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