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Acceleration

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Acceleration

10.3

- 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.

- 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)

- 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

- 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

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

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

- Page 388 questions 1, 2, 3, 4, 5

- 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).

Solving for vf use:

vf = vi + aavΔt

Solving for vi use:

vi = vf – aavΔt

Solving for t use:

t = Vf - Vi

a

- 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

- Page 388 and 389 questions 7 to 13