Question

A car accelerates from rest at a constant rate of $2m{s}^{-2}$ for some time. Then it retards at a constant rate of $4m{s}^{-2}$ and come to rest. It remains in motion for $6s$.

• A. Its maximum speed is $8m{s}^{-1}$
• B. It maximum speed is $6m{s}^{-1}$
• C. It travelled a total distance of $24m$
• D. It travelled a total distance of $18m$

Answer 1

Answer: (A), (C)

The correct options are
A Its maximum speed is $8m{s}^{-1}$
C It travelled a total distance of $24m$

$a_1=2m{s}^2,a_2=-4\frac{m}{s^2}$
$v_0=a_1{t}_1=2t_1,v_0=a_2{t}_2=4t_2$
$t_1+t_2=6\Rightarrow \frac{v_0}{2}+\frac{v_0}{4}=6$
$\Rightarrow v_0=8\frac{m}{s}$

Distance during constant accelerated motion can be calculated as $V_{avg}t$. So,
$AC=V_{avg}{t}_1=\frac{v_0+0}{2}{t}_1$
$CB=V_{avg}{t}_1=\frac{v_0+0}{2}{t}_2$

Total distance travelled
$S=AC+CB=\frac{1}{2}{v}_0{t}_1+\frac{1}{2}\times v_0{t}_2$
$\Rightarrow S=\frac{1}{2}{v}_0[t_1+t_2]=\frac{1}{2}\times 8\times 6=24m$