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The equations of motion (there are several) are also known as kinematic equations which descibe the mathematical relationships between variables such as distance, velocity, acceleration, and time. They can be used to determine how long it will take to go from one place to another; how fast a car was going when it hit a tree; how long it will take a falling object to hit the ground; how fast you will be going when you jump off the top of a building; and essentially any question relating to the motion of one or more objects. Suppose you want to travel to another city and need to get there in a certain time. You can calculate what you average speed must be if you drive non-stop or what it must be if you make stops along the way.
Have you ever pushed a supermarket trolley? Did you notice the fuller it gets the harder it is to push? This is Newtons 1st law of motion in action: F = ma. F = force (how hard you have to push), m = mass (how many groceries are in the trolley), a = acceleration (how quick you can get it moving from standstill). So, if you want to get your trolley moving to a reasonable speed, the more stuff you have, the harder you have to push.
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