Question

A car is moving with a velocity of 10 m/s. The driver sees a wall ahead of him and applied brakes. The car stops after covering $10m$ distance. If the car was moving with a speed pf $20m{s}^{-1}$, it would have stopped in $30m$ distance. The reaction of the driver is

• A. $0.5s$
• B. $0.6s$
• C. $0.7s$
• D. $1s$

Answer 1

The correct option is A $0.5s$

Case I. Suppose reduction time = t , so = 10 meters

then distance in t sec will be 10t meter

$\Rightarrow$ remaining distance = 10 meter - 10 t

using $v^2=u^2-2as$

we get $s=\frac{u^2-v^2}{2a}=\frac{(10{)}^2-0}{2a}=\frac{50}{a}$

$\Rightarrow \frac{50}{a}=10-10t$ _______ (1)

Case II

u=20 m/s & $S_0=30$ meter

distance in t sec will be 20 t meter

distance during retardation $S=\frac{u^2-v^2}{2a}=\frac{(20{)}^2-0}{2a}$

$S=\frac{200}{a}$

$S_0=30m\Rightarrow \frac{200}{a}+20t=30$

$\frac{50}{a}+5t=7.5$ _______ (2)

using (1) $\frac{50}{a}+10t=10$

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___________________

0-5t= -2.5 $\Rightarrow$ subtracting t=0.5 second