Introduction

When an object's velocity chages, it accelerates. Acceleration shows the change in velocity in a unit time. Velocity is measured in meters per second, m/s, so acceleration is measured in (m/s)/s, or m/s2, which can be both positive and negative

The average acceleration is the ratio between the change in velocity and the time interval:

acceleration

Example

If a car moves from the rest to 5m/s in 5 seconds, its average acceleration is:

acceleration

An instantaneous acceleration is the change in velocity at one moment.

Velocity-time Graph

Let's examine more about a velocity-time graph. We can say that the tangent of a velocity-time graph represents instantaneous acceleration since

acceleration

For example, the instantaneous acceleration when t = 3 at the below graph is 3 m/s2, since the graph has a slope of 3 when t = 3.

acceleration

Displacement and Constant Acceleration

In this section, we will assume that acceleration is always constant. We know that the area under the line of a velocity-time graph represents the displacement. Therefore, the equation

acceleration

is true, where Vi is the initial velocity and Vf is the final velocity, since the area of a triangle is 1/2 * width * height.

acceleration

The final velocity of a uniformly accelerated object is

acceleration

where:

  • Vf is the final velocity in m/s,
  • Vi is the initial velocity in m/s,
  • a is acceleration in m/s2, and
  • t is time in second.

Therefore, by substituting it to the previous equation,

acceleration

therefore, acceleration is true. If you don't understand the derivation, don't worry. The red formulae are the ones that you should learn.

From equations Formula for calculating displacement from initial and final velocity and Formula for calculating the final velocity from initial velocity, time, and acceleration, we can also say that

acceleration

Therefore, Formula illustrating the relationship between initial and final velocity, acceleration, and displacement is true. These four red equations are very important and you should be very familiar with them. (It doesn't mean that you should memorize these formulae. Learn by using them.)

Acceleration Due to Gravity

Galileo was the first to find out that all objects falling to Earth have a constant acceleration of 9.80 m/s2 regardless of their mass. Acceleration due to gravity is given a symbol g, which equals to 9.80 m/s2.

Therefore, if you drop a pen, it should behave like this...

Time (s) Velocity (m/s) Displacement (m)
000
19.84.9
219.619.6
329.444.1
439.278.4

For all previous equations, we can substitute g for a:

acceleration

acceleration

acceleration

References & Resources

  • http://library.thinkquest.org/10796/ch2/ch2.htm