Acceleration

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

$Ac\c\e\l\e\r\ation=((v_2-v_1))/t$

You may also see this written as

$Ac\c\e\l\e\r\ation=(Deltav)/t$

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?

Answer:

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

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

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 $12m//s$ ?

Answer:

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

$-0.04=((0-12))/(time)$

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

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

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?

Answer:

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

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!

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

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

$v_2-12.4=-32.4\ m//s$

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

NOTE:

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.