A car moving with a velocity of \(72 km / hr\) was brought to rest in \(10 s\) by a constant retarding force, what was the total distance covered during this time?
A. \(200 m\) B. \(50 m\) C. \(100 m\) D. \(125 m\)
Correct Answer: C
Explanation
$$ u=72 km / hr =\frac{72 \times 1000}{3600}=20 m / s $$ using Newton's equation of uniform acceleration \(v=u+a t \ldots \ldots(1)\) $$ \begin{aligned} &a=\frac{v-u}{t} \\ &a=\frac{0-20}{10}=\frac{-20}{10}, \end{aligned} $$ \(a=-2 m / s ^{2}\) (deceleration) thus; $$ \begin{aligned} &s=u t+1 / 2 a t^{2} \\ &s=20 \times 10+1 / 2(-2) \times 10^{2} \\ &s=200-100=100 m \end{aligned} $$ method \(-2\) using the velocity - time graph below distance travelled \(=\) area under the velocity time graph \(=\) area of a triangle $$ \begin{aligned} &s=1 / 2 \times b \times h \\ &s=1 / 2 \times 10 \times 20 \\ &=200 / 2=100 m \end{aligned} $$