The cyclist went down the hill in 10 seconds, moving with constant acceleration. Determine the length

| March 10, 2021 | education

The cyclist went down the hill in 10 seconds, moving with constant acceleration. Determine the length of the hill and the cyclist’s acceleration if at the beginning of the descent the speed was 18 km / h, and at the end of the descent 36 km / h.

To find the values of the length of the slide and the acceleration of the cyclist, we will use the formulas: S = L = (Vk + Vn) * t / 2 and a = (Vk – Vn) / t.

Values of variables: Vк – speed at the end of the hill (Vк = 36 km / h = 10 m / s); Vн – the initial speed of the cyclist (Vн = 18 km / h = 5 m / s); t is the duration of the cyclist’s descent (t = 10 s).

Calculation: a) Slide length: L = (Vк + Vн) * t / 2 = (10 + 5) * 10/2 = 75 m;

b) Cyclist acceleration: a = (Vk – Vn) / t = (10 – 5) / 10 = 0.5 m / s2.

Check: L = (Vk ^ 2 – Vn ^ 2) / 2a = (10 ^ 2 – 5 ^ 2) / (2 * 0.5) = 75 m (correct).

Answer: The length of the slide is 75 m; the cyclist descended along it with an acceleration of 0.5 m / s2.



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