# The skier covered a 100 m path in 20 s, moving with an acceleration of 0.3 m / s².

The skier covered a 100 m path in 20 s, moving with an acceleration of 0.3 m / s². What is the skier’s speed at the beginning and end of the path?

S = 100 m.

t = 20 s.

a = 0.3 m / s ^ 2.

V0 -?

V -?

For motion with constant acceleration, the following formulas are valid: S = V0 * t + a * t ^ 2, S = (V ^ 2 – V0 ^ 2) / 2 * a, a = (V – V0) / t.

V – V0 = a * t.

V – V0 = 0.3 m / s ^ 2 * 20 s = 6 m / s.

V ^ 2 – V0 ^ 2 = 2 * a * S.

Let’s write the difference of squares: V ^ 2 – V0 ^ 2 = (V – V0) * (V + V0).

2 * a * S = a * t * (V + V0).

V + V0 = 2 * S / t.

V + V0 = 2 * 100 m / 20 s = 10 m / s.

Let’s solve a system of 2 equations.

V – V0 = 6 m / s;

V + V0 = 10 m / s.

V = 6 + V0;

6 + V0 + V0 = 10.

2 * V0 = 4;

V0 = 2 m / s;

V = 6 + 2 = 8 m / s.

Answer: V0 = 2 m / s, V = 8 m / s.

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