Question

A car starts from rest, attains a velocity of $36 \,km\, h^{-1}$ with an acceleration of $0.2 \,m \,s^{-2}$, travels $9 \,km$ with this uniform velocity and then comes to halt with a uniform deceleration of $0.1 \,m \,s^{-2}$. The total time of travel of the car is

• A. $1050\,s$
• B. $1000\,s$
• C. $950\,s$
• D. $900\,s$

Answer 1

Answer: (A)

Let the car be accelerated from $A$ to $B$. It moves with uniform velocity from $B$ to $C$ and then moves with uniform deceleration from $C$ to $D$.
For the motion of car from $A$ to $B$,
$u=0$, $v=36\,km\,h^{-1}=36\times\frac{5}{18} m\,s^{-1}=10\,m\,s^{-1}$, $a=0.2\,m\,s^{-2}$
Time taken, $t_{1}=\frac{v-u}{a}=\frac{10\,m\,s^{-1}-0}{0.2\,m\,s^{-2}}=50\,s$
For the motion of car from $B$ to $C$
$S = 9\,km = 9000\, m$
Time taken, $t_{2}=\frac{9000\,m}{10\,m\,s^{-1}}=900\,s$
For the motion of car from $C$ to $D$,
$v=0$, $u=10\,m\,s^{-1}$, $a=-0.1\,m\,s^{-2}$
Time taken, $t_{3}=\frac{0-10\,m\,s^{-1}}{-0.1\,m\,s^{-2}}=100\,s$
Total time taken $= t_1 + t_2 + t_3$ ;
$= 50\, s + 900\, s + 100\, s = 1050 \,s$