A sprinter running a 100 m race starts at rest, accelerates at constant acceleration of magnitude A for 2 seconds, then runs at a constant speed until the end. Find the position (relative to the start) and speed of the runner at the end of the 2 seconds, in terms of A.

Respuesta :

Answer:

The distance ran by the runner in the 2 seconds is 2·A

The speed of the runner at the end of the 2 seconds is 2·A

Explanation:

The given information are;

The distance the sprinter is running = 100 m

The initial constant acceleration of the sprinter, a = A

The duration of the initial acceleration, t = 2 s

The initial speed of the printer, u = 0 (The sprinter starts from rest)

The rate with which the sprinter then runs with to the end = Constant speed

Therefor, we have, from the equation of motion;

s = u × t + 1/2 × a × t²

Where;

s = The distance ran by the sprinter

∴ at t = 2 seconds, we have;

s = 0 × 2 + 1/2 × A × 2² = 1/2 × A × 4 = 2·A

The distance ran by the runner in the 2 seconds = 2·A

The speed, v, of the runner at the end of the 2 seconds is given as follows;

v = u + a × t

When t = 2 seconds, we have;

v = 0 + A × 2 = 2·A

The speed of the runner at the end of the 2 seconds = 2·A.