Mammoth Memory


Acceleration is a change in velocity. However it can sometimes be easier to think of it as a change in speed. How much an object accelerates depends on how quickly its velocity/speed changes.

The units for acceleration are usually metres per second per second (m/s/s) or metres per second squared (m/s2).

The formula used to calculate acceleration is:

The acceleration formula is change in velocity divided by time



You may also see this written as


Acceleration is change in velocity over time 

Accelerator pedal to the floor changes speed to stay on time.


Example 1

A cyclist increases her speed from `5m//s` to `19m//s` in `7s`. What is her acceleration?


`Ac\c\e\l\e\r\ation=(chan\g\e\ \ i\n\ \ velocity)/(time)` 

`Ac\c\e\l\e\r\ation=((19-5))/7=14/7=2\ m//s^2` 



Example 2

An oil tanker decelerates at an average rate of `0.4m//s^2`. How long to the nearest minute would it take to come to a complete stop if it was initially travelling at `12m//s`?


`Ac\c\e\l\e\r\ation=(chan\g\e\ \ i\n\ \ velocity)/(time)` 


`time=((0-12))/-0.04=(-12)/-0.04=300\ \ se\c\o\nds`

`300/60=5\ m\i\n\u\tes`


Example 3

A goalkeeper takes a goal kick and the ball travels away from goal. When it reaches an opposing striker at a velocity of `12.4m//s` the ball is kicked back towards goal by the striker. This results in the ball accelerating at `72m//s^2` towards the goal for the `0.45` seconds during which the striker's foot is in contact with the ball. At what velocity does the ball leave the striker’s foot?


`Ac\c\e\l\e\r\ation=(chan\g\e\ \ i\n\ \ velocity)/(time)` 

Multiply both sides by time to make change in velocity the subject,

`Ac\c\e\l\e\r\ationtimestime=(chan\g\e\ \ i\n\ \ velocitytimescancel(time))/(cancel(time))` 

`chan\g\e\ \ i\n\ \ velocity=Ac\c\e\l\e\r\ationtimestime` 


However there is a trick in this question! The ball is initially traveling away from goal and then accelerates towards goal, this means the acceleration is in the opposite direction and therefore is in a negative direction!

`chan\g\e\ \ i\n\ \ velocity=-72times0.45=-32.4\ m//s` 

`chan\g\e\ \ i\n\ \ velocity=v_2-v_1`

`v_2-12.4=-32.4\ m//s` 

`v_2=-32.4+12.4=-20\ m//s`



The velocity is negative as the direction the ball travels after the striker kicks it is opposite to the direction it was travelling when the goalkeeper kicked it.

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