In case of emergency braking, the braking distance of the vehicle should not exceed 30m.

In case of emergency braking, the braking distance of the vehicle should not exceed 30m. How fast can a car move if the coefficient of sliding friction between its tires and the road is 0.5?

S = 30 m.

V = 0 m / s.

g = 9.8 m / s ^ 2.

μ = 0.5.

V0 -?

The acceleration of the body a during deceleration is expressed by the formula: a = (V0 ^ 2 – V ^ 2) / 2 * S, where V0, V are the initial and final speeds during deceleration, S is the path traveled by the body during deceleration.

Since the car has stopped, V = 0 m / s.

a = V0 ^ 2/2 * S.

V0 = √ (2 * a * S).

m * a = Ftr.

N = m * g.

Ftr = μ * N = μ * m * g.

m * a = μ * m * g.

a = μ * g.

V0 = √ (2 * μ * g * S).

V0 = √ (2 * 0.5 * 9.8 m / s ^ 2 * 30 m) = 17 m / s.

Answer: the maximum vehicle speed is V0 = 17 m / s.