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I have a science question to answer, and just need some things cleared up. The question states: 'If a sprinter starts out of the blocks and speeds up to reach a top speed of 15m/s in 5 seconds, what is their acceleration?' I answered 3m/(s squared). The second part of the question asks- 'If the sprinter's mass is 70kg, how much force is needed for him to accelerate at that rate?' My guess was 210 newtons. But I am unsure. My reasoning was that 70 newtons will make him move 1m/s. So I answered 210 newtons to make him move at 3m/(s squared).

However, I have a (very strong) feeling I'm wrong. I just need the math cleared up. If you could point out the flaws in my reasoning/calculations, feel free to do so, and could you also explain the correct way to do it?

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    $\begingroup$ You're right because $F = ma$. $\endgroup$ – PiKindOfGuy Mar 24 at 22:15
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I will try to cover all the aspects related to your question to clear both any physics and math questions you may have.

First of all, the acceleration is always defined as the rate of change of velocity per unit of time, that is, how much has velocity changed in a certain period of time. Without introducing notions of calculus, you can always calculate it as,

$$\vec{a}=\frac{\vec{v_f}-\vec{v_0}}{t_f-t_0}$$where the subindices $f$ and $0$ denote the final and initial values, respectively. So from your example, you can see that you indeed the acceleration you calculated is correct.

Now, the second law of Newton states that the acceleration that a body experiences is directly proportional to the force applied in that direction and inversely proportional to the object's inertial mass. In other words, the stronger the force, the more the object accelerates, and the more massive the object, the less it accelerates. This can be written in the classical equation,

$$\vec{a}=\frac{\vec{F}}{m}$$

or solving for the force, you recover the well-known,

$$\vec{F}=m\vec{a}$$

This allows you to calculate the force necessary for an object of certain mass $m$ to reach a certain acceleration $\vec{a}$, independent of the origin of the force. In other words, you don't need to worry about the nature of the force or how you will eventually reach that acceleration, as this equation will allow you to calculate the total net force to reach such acceleration. Therefore, you can see from your example that your result is also correct.

Now as an exercise to test how well you understood these topics, I'll like to propose you the following questions in continuation of your problem:

a) If the man reaches the same top speed in half the time (that is, he reaches 15 m/s in 2.5 seconds), what's the new acceleration?

b) If the man now weights half of the mass given in the statement (that is, 35 kg), how much force is needed for him to accelerate at that rate?

c) Compare your new results with the previous ones.

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