All students Rates of Change, Velocity, Acceleration

A rate of change is the amount a quantity changes divided by the the time it takes the change to occur. More formally this is the rate of change with respect to time.

For example, velocity is the rate of change of position. It equals change in position/time it took to move or

or v = change in position/change in t

One can take a rate of change and the time and use it to find the change in a quantity: change = rate of change * time it took

For example change in position = v * change in t [* means multiply]

Velocity is not constant if uncancelled forces are present (net force actually). The rate of change of velocity is called acceleration, a.

a = change in v/ change in t change in v = a * change in t.

An example of this is a book on a table, the table pushes up on the book as hard as gravity pulls down on it so the forces cancel. Take away the table and it falls, but not at a constant rate. It starts out with v initial = 0 and then falls with increasing velocity falling faster and faster until it hits the floor and the floor's upward force stops its motion and cancels gravity. Do you think the force on the book when it first hits the floor is much greater than when the book is at rest on the floor? Think about it. Did the floor create a very large change in the book's velocity at first. Would this require a large upward force?