A car is moving with speed $20 m / s$ . Suddenly the driver sees the sign of danger at a distance of $50 m$ ; after a certain reaction time $t_{0}$ he applies brakes to cause deceleration $5 m / s^{2}$ . What is the maximum allowable reaction time $t_{0}$ to avoid accident and distance travelled by the during reaction time?

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Solution

Given,

$S p e e d = 20 m / s, d = 50 m, r e t a r d a t i o n = 5 m / s^{2}$

Let the ppossible reaction time be $t_{s}$ So the car moves $20 t$ m And applied breaks with retardation $5 m / s^{2}$

So, the total distance under retardation is $\leq 50$ m

Thus the distance under the application of retardation $= \frac{20^{2} - 0^{2}}{2 \times 5} = s^{'} \Rightarrow s^{'} = 40 m$

Therefore, $20 t_{s} + 40 \leq= 50 \Rightarrow 20 t_{s} \leq 50 - 40 \Rightarrow 20 t_{s} = 10 \Rightarrow t_{s} \leq \frac{1}{2} \leq 0.5 s$

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A car is moving with speed 20m/s. Suddenly the driver sees the sign of danger at a distance of 50m; after a certain reaction time t0 he applies brakes to cause deceleration 5m/s2. What is the maximum allowable reaction time t0 to avoid accident and distance travelled by the during reaction time?