# A motor car movin

Time required by the truck to reach 0 km/h (t1) = 5s

Initial speed of the truck (u) = 72 km/h = 20 m/s

Final speed (v) = 0 m/s

Deceleration of the truck ( �atruck) can be calculated using equations of motion.

(Negative sign denotes deceleration/retardation)

For the car, time required to stop = 3s

We can find the deceleration of the car similarly to how we found of the truck above.

The human response time is 0.5s. This means after the truck gives signal, the car will begin to retard after 0.5 seconds. For these 0.5 seconds, the car will move at a uniform speed.

Let the car be at a distance ‘x’ when the truck gives the signal and ‘t’ be the time taken to cover this distance.

Velocity of car (v,) after time t will be

Velocity of truck after time t (v,,)

For avoiding the car to bump into the truck

On solving for t, we get

Distance travelled by the truck in t = 1.25 seconds (s1)

Distance travelled by the car in time t is the sum of the distance travelled by the car with uniform velocity for 0.5 seconds and the distance travelled by the car while retarding for (t – 0.5) seconds (s2)

Safe distance = s2 – s1 = (23.125 – 21.875) m = 1.25 m

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