Question

A body travelling along a straight line traverse one-third the distance with a velocity of $5m/s$ . The remaining part of the distance was covered with velocity $3m/s$ for half the time and with velocity $2m/s$ 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)

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
$v=\frac{x}{\frac{x}{5}}$
$v=5m/s$