When braking from a speed of 40 km / h to a complete stop, the car traveled a distance of 16 m.

| July 5, 2021 | education

When braking from a speed of 40 km / h to a complete stop, the car traveled a distance of 16 m. How far this car will travel on the same road when the speed decreases from 100 km / h to 60 km / h. Assume that the acceleration during braking is constant and the same in both cases.

V10 = 40 km / h = 11.1 m / s.

V1 = 0 m / s.

S1 = 16 m.

V20 = 100 km / h = 27.8 m / s

V2 = 60 km / h = 16.7 m / s.

a1 = a2.

S2 -?

With uniformly accelerated braking, the path of the car S is expressed by the formula: S = (V0 ^ 2 – V ^ 2) / 2 * a.

S1 = (V10 ^ 2 – V1 ^ 2) / 2 * a1.

Since the final speed of the car is V1 = 0 m / s, the formula will take the form: S1 = V10 ^ 2/2 * a1.

Let us express the acceleration of the car: a1 = V10 ^ 2/2 * S1.

S2 = (V20 ^ 2 – V2 ^ 2) / 2 * a2.

Since a1 = a2 by condition, then S2 = (V20 ^ 2 – V2 ^ 2) / 2 * a1 = 2 * S1 * (V20 ^ 2 – V2 ^ 2) / 2 * V10 ^ 2 = S1 * (V20 ^ 2 – V2 ^ 2) / V10 ^ 2.

S2 = 16 m * ((27.8 m / s) ^ 2 – (16.7 m / s) ^ 2) / (11.1 m / s) ^ 2 = 64 m.

Answer: when braking, the car will travel S2 = 64 m.



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