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It makes sense that if something has a greater mass, it would take a larger force to give it the same acceleration as something with less mass. First of all lets take a look at them:. As you probably already know, velocity divided by time is equal to acceleration and velocity multiplied by time is equal to displacement. This means that on a speed vs. If you have an initial velocity and a final velocity the graph would look something like this:. As I previously said, the gradient of the line is equal to acceleration.

We know that the area under the graph is equal to the displacement. So we know that multiplied by gives us the bottom rectangle of the area and divided by 2, gives us the top triangle.

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This gives us:. Now we already know that so we can rearrange that to give and then substitute this into our equation for displacement. From this we have. If we just multiply out the bracket that provides us with our second formula:. For those of you who like to find maths where they can, you might be interested to know that is the integral of with respect to. Now those of you who are keen on spotting patterns may have noticed that this equation looks a lot like the last one.

If you rearrange to make the subject you get:. Now you just need to integrate this result with respect to time to give you our 3rd equation:. There are a couple of rules, for instance they can only be used in cases where there is constant acceleration.

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The urban issues writer talks to us about his love of writing about highways — for good and evil! Head-on bicycle crash shows the need for more bike infrastructure.

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