Acceleration
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Acceleration. 10.3. Definition. The term acceleration describes all situations in which the speed is changing or acceleration (a) is the rate of change in speed. To solve this we examine the ratio of the change in speed ( Δ v) to the time interval ( Δ t) during which this change occurred.

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Acceleration

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Acceleration

Acceleration

10.3


Definition

Definition

  • The term acceleration describes all situations in which the speed is changing or acceleration (a) is the rate of change in speed.

  • To solve this we examine the ratio of the change in speed (Δv) to the time interval (Δt) during which this change occurred.


Uniform a vs average a

Uniformavs. Averagea

  • When the ratio remains constant throughout acceleration, the same change in speed (Δv) occurs at each equal interval of time (Δt).

  • We call this uniform or constant acceleration, and this can be represented by:

Δv

a =

Δt

If an object is travelling 4.5 m/s for a time of 1s, what is the objects acceleration?

After 2s? (assume uniform a)

After 3s? (assume uniform a)


Meters per second per second

Meters per second per second??

  • You will notice that when we perform our calculations you may end up with .

  • This is then simplified to m/s2. You may also end up with kilometers per hour over seconds, in which case we say kilometers per hour per second (km/h)/s.

m/s

s


Uniform a vs average a1

Uniforma vs. Averagea

  • However, when acceleration varies over a period time, we tend to talk about the object’s average acceleration, and is represented by:

Δv

aav =

Δt


Cancelling units

Cancelling units

  • When solving for Δt or Δv your units will need to be reduced or cancelled.


A few helpers

A few helpers

Δv

When solving for acceleration use:

a =

Δt

When solving for Δv (change in speed) use:

Δv =

a•

Δt

When solving for Δt (change in time) use:

Δv

Δt =

a


Your turn

 Your Turn 

  • Page 388 questions 1, 2, 3, 4, 5


Refining the acceleration equation

Refining the Acceleration Equation

  • In the real world initial speed and final speed is a known value, so when representing this in an equation we must take this into account.

  • The acceleration equation can be more precisely written as:

v2 – v1

aav =

Δt

NOTE:

v2 and v1 are often times represented by vf (final speed) and vi (initial speed).


Some more helpers

Some more HELPERS!

Solving for vf use:

vf = vi + aavΔt

Solving for vi use:

vi = vf – aavΔt

Solving for t use:

t = Vf - Vi

a


Slowing down

Slowing Down

  • There is no difference in the procedure for slowing down, it is still a change in speed. The only difference will be that slowing down is represented by a negative (-) acceleration

For example, when a car comes to a stop the v1 will be your speed when you apply the brakes and v2 will be zero. This (v2 – v1) will give you a negative acceleration


Your turn again

Your Turn Again

  • Page 388 and 389 questions 7 to 13


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