Question

A body starts from rest with a uniform acceleration of $2m{s}^{-2}$ for 10 s, it moves with constant speed for 30 s then declerates by $4m{s}^{-2}$ to zero. the distance covered by the body is _____m

Answer 1

Answer: 750

$u=0,a=2m{s}^{-2},t=10s$
$\therefore s_1=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}\times 2\times 100=100m$
Velocity after $10s,$
$\upsilon =u+at=0+2\times 10=20m{s}^{-1}$
$\therefore s_2=\upsilon \times 30=20\times 30=600m$
Final velocity $=0,a=-4m{s}^{-2}$
$\therefore 0={\upsilon }^2+2a{s}_3$
$0={\left(20\right)}^2-2\times 4\times s_3$
$\therefore s_3=\frac{400}{8}=50m$
$\therefore s=s_1+s_2+s_3=100+600+50=750m$