Question

A car accelerates from rest with $2 \,m / s ^{2}$ on a straight line path and then comes to rest after applying brakes. Total distance travelled by the car is $100\, m$ in $20$ seconds. Then, the maximum velocity attained by the car is

• A. 10 m / s
• B. 20 m / s
• C. 15 m / s
• D. 5 m / s

Answer 1

Answer: (A)

Given,
Acceleration of car $(\alpha)=2\, m / s ^{2}$
Distance covered by car in $20$ seconds $(s)=100\, m$
We know that.
$ s =\frac{1}{2} \cdot \frac{\alpha \beta}{\alpha+\beta} t^{2} $
$ 100 =\frac{1}{2} \times \frac{2 \beta}{(2+\beta)} \times 20 \times 20 $
$ \frac{100}{400} =\frac{\beta}{(2+\beta)} $
$\Rightarrow \frac{1}{4}=\frac{\beta}{2+\beta}$
$ \Rightarrow 4 \beta=2+\beta $
$\Rightarrow 3 \beta=2$
$ \Rightarrow $ retardation $ \beta=\frac{2}{3} m / s ^{2}$
$\therefore $ Maximum velocity $\left(v_{\max }\right)=\frac{\alpha \beta t}{\alpha+\beta}$
$ \frac{2 \times \frac{2}{3} \times 20}{2+\frac{2}{3}}=\frac{\frac{80}{3}}{\frac{8}{3}}=\frac{80}{3} \times \frac{3}{8} $
$=10\, m / s $