Question

Position of a particle moving along $x$-axis is given by $x=3 t-4 t^{2}+t^{3}$, where $x$ is in metre and $t$ in seconds. Find the average velocity of the particle in the time interval from $t =2\, s$ to $4\, s$.

• A. 7 m/s
• B. 9 m/s
• C. 13 m/s
• D. none of these

Answer 1

Answer: (B)

Rate of change of displacement is velocity,
i.e., $v=\frac{d x}{d t} v=\frac{d x}{d t}=3-8 t+3 t^{2}$
Given, $x=3 t-4 t^{2}+t^{3}$
$v=\frac{d x}{d t}=3-8 t+3 t^{2}$
At $t=2, v_{1}=3-16+12=-1$
At $t=4, v_{2}=3-32+48=19$
Average velocity $=\frac{v_{1}+v_{2}}{2}=\frac{-1+19}{2}$
$=9\, m / s$