Question

A body travelling along a straight line traverse one-third the distance with a velocity of $5 \,m/s$ . The remaining part of the distance was covered with velocity $3 \,m/s$ for half the time and with velocity $2 \,m/s$ for the other half of the time. The average velocity of the body over the whole time of motion will be

• A. $3\, m/s$
• B. $5\, m/s$
• C. $2\, m/s$
• D. $2.5\, m/s$

Answer 1

Answer: (B)

$5\, m/s$

Answer 2

Time taken in the one third part of total distance coverd is $t_1$ and for remaining part is $2t_2$
$t_1 = \frac{x/3}{5} = \frac{x}{15}$
$x_1 + x_2 = \frac{2}{3} x$
$3t_2 + 2t_2 = \frac{2}{3} x$
$5t_2 = \frac{2}{3}x$
$t_2 = \frac{2x}{15}$
Total time $= t_1 + 2t_2$
$= \frac{x}{15} + \frac{2x}{15}$
$t = \frac{3x}{15} = \frac{x}{5}$
Average velocity
$v = \frac{x}{\frac{x}{5}}$
$v = 5\,m/s$