Acceleration
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Acceleration is the rate of change in speed. It is determined by the ratio of the change in speed(v) to change to the time(t) during this change occurred.

A= v/t or Aav= v/t

If the ratio remains constant throughout the acceleration, then the acceleration is called constant. In constant acceleration, the same change in speed occurs at each internal of time (t).

When an object's acceleration varies over a period a time, it can be described as average acceleration. Average acceleration is the average change in spee dof a object.

For the next example you must assume the acceleration is constant.

Sample: (finding average acceleration)

Lets assume your in a boat, docked on the harbor front of Lake Ontario and you want to boat down to Niagara Falls. You accelerate from rest (0m/s) to 80 m/s in 4s. What is your acceleration?

Step one: State given

v = 80.0 m/s
t = 4 s
Aav = ?

Step 2: State the equation
Aav =v/t

Step 3: replace the equation with the values given

Aav = 80.0m/s / 4s
Aav =20m/s a second

Step 4: State a word answer.

The boat increases in speed by 20m/s every second.

So, in three seconds the boat can accelerate to 60 m/s, and by 4 seconds it can accelerate to 80m/s. The acceleration can be converted to 20m/s2.

Sample 2 (finding change in speed)

Kevin was chased by a man eating gorilla at an average acceleration of 4m/s2 for 40s. What was her change in speed at the end of the 40is

Step 1: State the Given

v =?
t=40s
Aav = 4m/s2

Step 2: State the equation

Aav =v/t
*we need to find the v so we must redefine the equation
v = Aavt

Step 3: replace the equation with the given values

v = 4m/s2 x 40 s
v = 160m/s

Step 4: State the answer in sentence form

Kevin's change in speed was 160m/s

Sample 3 (Finding change in time)

After being chased by that man eating gorialla Kevin decided to run the rest of the way back to camp. His average acceleration was .50m/s2 and his change in speed was 4.6m/s

Step 1: State given

v =4.6m/s
t = ?
Aav = .50m/s2

Step 2: State the equation

Aav =v/t
*we need to find the t so we must redefine the equation
t =v/Aav

Step 3: Fill in the numbers with the information

t = 4.6m/s / .50m/s2
t = 9.2s

Step 4: Write the answer in sentence form

The change in time is 9.2 seconds.

Refining the acceleration equation

As you remember from the distance-time graph, to calculate d you can by subtracting d1 from d2. The same can be done for v, it can be derived from subtracting v1 from v2.
v1 being the starting speed and v2 being the ending speed.
(v = v2 - v1)

Therefore the equation can be changed to:

Aav = (v2-v1) / t

Sample 4

Lets say that from a cruising speed of 4m/s you decide to speed up in your brand new scooter. 6s later your you have accelerated to 20m/s. What is your average speed?

Step 1: State the given

v1 = 4m/s
t= 8s
v2 = 20m/s
Aav = ?

Step 2: State the equation

Aav =(v2 - v1)/t

Step 3: Fill in the given values into the equation

Aav = (20m/s - 4m/s) /8s
Aav = 2s2

Step 4: State the answer in sentence form

The average acceleration is 2ms2

When asked to find the value of v1 when v2, aav, and t values are given the equation is:
v1 = v2 -aav x t

When asked to find the value of v2 when v1, aav, and t values are given the equation is:
v2 = v1 + aav x t

It is also possible to have a negative acceleration, when you see a car slow down the acceleration is decreasing.

Sample 5

A car decelerated from 50m/s to 0 m/s in 5 seconds. What was the cars acceleration?

Step 1: State Given

v1 = 50
v2 = 0
t= 5s
Aav = ?

Step 2: State equation

Aav = v2-v1/t

Step 3: Fill in equation with the given values

Aav = (0m/s - 50m/s) / 5
Aav = -10 m/s2

Step 4: State the answer in sentence form.

The car decelerated at -10m/s2

Continue to the next lesson: ::Speed-Time Graphs::