A car driver, driving along a country road at a speed of 25 m / s, sees a sign ahead limiting

univerkov | May 25, 2021 | education

A car driver, driving along a country road at a speed of 25 m / s, sees a sign ahead limiting the speed to 60 km / h (16.6 m / s). Does the driver manage to reduce the speed to the specified limit if the maximum steady-state deceleration of the car in the given road conditions is 5 m / s2; t1 = 1.2 s; t2 = 0.2 s; t3 = 0.2 s, and the distance to the sign is 65 m? How long does it take for the car to move at the specified distance?

V0 = 25 m / s.

V = 60 km / h = 16.6 m / s.

a = 5 m / s2.

S “= 65 m.

t -?

We will assume that when braking, a passenger car moves at uniform acceleration. The braking path S is expressed by the formula: S = (V0 ^ 2 – V ^ 2) / 2 * a.

S = ((25 m / s) 2 – (16.6 m / s) ^ 2) / 2 * 5 m / s2 = 35 m.

We see that with such an acceleration the car will reduce its speed through S = 35 m, and the distance to the sign is S “= 65 m.

The braking time t of a passenger car is expressed by the formula: t = (V0 – V) / a “.

a “= (V0 ^ 2 – V ^ 2) / 2 * S”.

a “= ((25 m / s) ^ 2 – (16.6 m / s) ^ 2) / 2 * 65 m = 2.7 m / s2.

t = (V0 – V) / a “.

t = (25 m / s – 16.6 m / s) / 2.7 m / s2 = 3.1 s.

Answer: the driver will have time to reduce the speed to the mark, t = 3.1 s.