# The cyclist moves downhill at a speed of 0.2 m / s2. What speed will the cyclist acquire in 10 s if his initial

The cyclist moves downhill at a speed of 0.2 m / s2. What speed will the cyclist acquire in 10 s if his initial speed is 5 m / s? How far has he traveled?

a = 0.2 m / s2.

V0 = 5 m / s.

t = 10 s.

V -?

S -?

According to the definition, acceleration a shows how the speed of a body changes over time. When braking, acceleration a is determined by the formula: a = (V0 – V) / t, where V0, V is the cyclist’s speed at the beginning and end of the ascent, t is the time the speed changes or the time of movement along the ascent.

V = V0 – a * t.

V = 5 m / s – 0.2 m / s2 * 10 s = 3 m / s.

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

S = ((5 m / s) ^ 2 – (3 m / s) ^ 2) / 2 * 0.2 m / s2 = 40 m.

If the cyclist was moving downhill, then V = V0 + a * t, S = (V ^ 2 – V0 ^ 2) / 2 * a.

V = 5 m / s + 0.2 m / s2 * 10 s = 7 m / s.

S = ((7 m / s) ^ 2 – (5 m / s) ^ 2) / 2 * 0.2 m / s2 = 60 m.

Answer: when ascending V = 3 m / s, S = 40 m, while descending V = 7 m / s, S = 60 m.

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