A sportsman skied down a 40 m long mountain in 5 seconds, determine the acceleration

A sportsman skied down a 40 m long mountain in 5 seconds, determine the acceleration and speed of the sportsman at the foot of the mountain.

S = 40 m.

t = 5 s.

V0 = 0 m / s.

a -?

V -?

We will assume that the athlete is moving uniformly.

The path S, with uniformly accelerated movement, is determined by the formula: S = V0 * t + a * t ^ 2/2, where V0 is the athlete’s initial speed, t is the descent time, a is the descent acceleration.

Since the skier starts his movement from a state of rest V0 = 0 m / s, the formula will take the form: S = a * t ^ 2/2.

a = 2 * S / t ^ 2.

a = 2 * 40 m / (5 s) ^ 2 = 3.2 m / s2.

The acceleration of the body a shows how the speed of the body changes during movement, and is determined by the formula: a = (V – V0) / t.

V = V0 + a * t.

V = 0 m / s + 3.2 m / s2 * 5 s = 16 m / s.

Answer: the athlete moves with acceleration a = 3.2 m / s2, at the end of the descent he will have a speed V = 16 m / s.