Question

A particle moves in a straight line with a velocity $v_t=\left|t-4\right|$ $m/s$ where $t$ is time in seconds. The distance covered by the particle in $8s$ is

• A. $8m$
• B. $16m$
• C. $4m$
• D. $2m$

Answer 1

The correct option is B $16m$

$V=|t-4|$

$V=t-4$ for $t>4$

$V=-(t-4)$ for $t<4$

For $t\in [0,4]$

$v=-t+4$

$a=-1m/s^2$

Since acceleration is uniform at $t=0,v=4m/s$

$x=\frac{1}{2}\times 1\times 16$

$x=8m$

For $t>0$, $v=t-4$

Acceleration $=1m/s$

$s=\frac{1}{2}\times 4\times 4=8m$

Total distance $=16m$