Question

A soccer player kicks a soccer ball (m = 0.42 kg) accelerating from rest to 32.5m/s in 0.21s. Determine the force that sends soccer ball towards the goal.

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Answer 1

F=65 N

Step-by-step explanation:

Uniform Acceleration

When an object changes its velocity at the same rate, the acceleration is constant.

The relation between the initial and final speeds is:

`v_f=v_o+a.t`

Solving for a:

`\displaystyle a=(v_f-v_o)/(t)`

Where:

vf = Final speed

vo = Initial speed

a = Constant acceleration

t = Elapsed time

The ball is kicked from rest vo=0 to vf=32.5 m/s in t=0.21 s. Computing the acceleration:

`\displaystyle a=(32.5-0)/(0.21)`

`a=154.8\ m/s^2`

Note: We have shown this result rounded to the nearest tenth, but we kept all the decimals in a scientific calculator for further calculations.

The force needed to accelerate the soccer ball is calculated by:

F = ma

The ball has a mass of m=0.42 kg, thus:

F=0.42*154.8

F=65 N

As mentioned, this result can only be obtained by keeping full precision in the above calculations.