The athlete runs 100m in 10s. The first 10 meters after the start, he runs with constant acceleration, the rest of the distance

| August 2, 2021 | education

The athlete runs 100m in 10s. The first 10 meters after the start, he runs with constant acceleration, the rest of the distance at a constant speed. Find acceleration for the first 10 meters and speed for the rest of the distance.

Task data: S (total length of the distance) = 100 m; t (total running time) = 10 s; S1 (first part of the distance) = 10 m.

1) Time in the first section:

1 equation: S1 = a * t12 / 2, whence we express: a = 2 * S1 / t1 ^ 2.

Equation 2: S2 = S – S1 = V * t2 = a * t1 * (t – t1) = 2 * S1 / t1 ^ 2 * t1 * (t – t1) = 2 * S1 / t1 * (t – t1) …

90 = 2 * 10 / t1 * (10 – t1).

90t1 = 20 * (10 – t1).

90t1 = 200 – 20t1.

110t1 = 200.

t1 = 200/110 = 1.818 s.

2) Acceleration on the first 10 meters: a = 2 * S1 / t1 ^ 2 = 2 * 10 / 1.8182 = 6.05 m / s2.

3) Speed at the rest of the distance: V = a * t1 = 6.05 * 1.818 = 11 m / s.



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