In physics, we say that a body has acceleration when there is a change in the velocity vector, either in magnitude or direction. In this section, we are going to study the concept of average acceleration, which represent the variation in velocity that, on average, takes place in a time interval.

## Average Acceleration

Average acceleration between two points P1 and P2 is defined as the ratio of the variation of the velocity and the time used to complete the motion between both points:

${\stackrel{\to }{a}}_{a}=\frac{{\stackrel{\to }{v}}_{2}-{\stackrel{\to }{v}}_{1}}{{t}_{2}-{t}_{1}}=\frac{∆\stackrel{\to }{v}}{∆t}$

where:

• ${\stackrel{\to }{a}}_{a}$ : Is average acceleration of the body
• ${\stackrel{\to }{v}}_{1}$ ,${\stackrel{\to }{v}}_{2}$ : Velocity vectors of points P1 and P2 respectively
• t1,t2: Initial and final times respectively
• $∆\stackrel{\to }{v}$ : Variation of the velocity between the initial and final points P1 and P2
• $∆t$ : Time spent in completing the motion between P1 and P2

Additionally, the average acceleration vector satisfies the following:

• The dimensional equation of the average acceleration is [aa] = [LT-2]
• The unit of measurement in the International System (S.I.) of the acceleration is meter per second squared (m/s2). A body with a 1 m/s2 acceleration changes its velocity by 1 meter/second every second
• Its magnitude (the "size" of the vector) is equal to the magnitude of the velocity variation vector divided by the elapsed time
• Its direction is the same as the direction of the velocity variation vector

It is important to remember that motion, which is colloquially called "braking", is also considered accelerated motion in physics, because in the end, the velocity vector is changing (specifically deceasing its magnitude).

## Solved exercises worksheet

Here you can test what you have learned in this section.

#### Acceleration in a basketball throw

difficulty

A basketball player throws the ball with a velocity of , with such bad luck that it bounces off the board with a velocity .

Calculate the average acceleration knowing that the impact against the board lasts exactly 0.02 seconds

## Formulas worksheet

Here is a full list of formulas for the section Average Acceleration. By understanding each equation, you will be able to solve any problem that you may encounter at this level.

Click on the icon   to export them to any compatible external program.

#### Average Acceleration

${\stackrel{\to }{a}}_{a}=\frac{{\stackrel{\to }{v}}_{2}-{\stackrel{\to }{v}}_{1}}{{t}_{2}-{t}_{1}}=\frac{∆\stackrel{\to }{v}}{∆t}$