A car is moving with a velocity of $20\text{m/sec}$. The driver sees a stationary truck at a distance of $100\text{m}$ ahead. After some reaction time $\Delta t$ he applies the brakes, produces a retardation of $4{\text{m/s}}^2$. The maximum reaction time to avoid collision will be

The correct option is B $2.5\text{sec}$
Car covers a distance $s$ before coming to rest using relation as $v^2=u^2+2as$
$\Rightarrow s=\frac{20\times 20}{4\times 2}=50\text{m}$
To avoid the clash the remaining distance $100-50=50\text{m}$ must be covered by the car with uniform velocity $20\text{m/s}$ during the reaction time $\Delta t$
Hence, $\frac{50}{\Delta t}=20$ or $\Delta t=\frac{50}{20}=2.5\text{sec}$