Question

A body moving along a straight line travels one third of the total distance with a speed of 3.0 m s^-1. The remaining distance is covered with a speed of 4.0 m s^-1 for half the time and 5.0 m s^-1 for the other half of the time. The average speed during the motion is

• A. 4.0 m s^-1
• B. 6.0 m s^-1
• C. 3.8 m s^-1
• D. 2.4 m s^-1

Answer 1

Answer: (C)

3.8 m s^-1

Answer 2

Let s be the total distances travelled by the body. Let $t_{1}$be the time taken to cover the first one their of the distance. Then

$t_{1} = \frac{S/3}{3} = \frac{S}{9}$

Let $t_{2}$be the time taken for each of the remaining two journeys. Then

$S - \frac{S}{3} = 4t_{2} + 5t_{2}$or$\frac{2s}{3} = 9t_{2}$or $t_{2} = \frac{2S}{27}$

Average speed $= \frac { \text { Total dis tan ce traveled } } { \text { Total time taken } } = \frac { \mathrm { S } } { \mathrm { t } _ { 1 } + 2 \mathrm { t } _ { 2 } }$ $\frac{S}{\frac{S}{9} + 2\left( \frac{2S}{27} \right)} = 3.8ms^{- 1}$