Acceleration Mini Lesson

Acceleration: average and instantaneous

We remember acceleration

​acceleration = change in velocity over time

Some text here about the topic of discussion

Question:

• when you think of acceleration what comes to mind?​

What qualifies as acceleration?

​

Answer:

• 3 ways that an object can accelerate include:

  • speeding up

  • slowi​ng down

  • changing direction

What qualifies as acceleration?

​

​These graphs are used when an object travels in a straight line and does NOT change direction.

• ​line A = acceleration (speeding up)

• line B = moving at a constant velocity (no change in speed)​

• line C = decelerating (slowing down)​

​Velocity vs Time Graphs

​A

​B

​C

​What about the slope of a Vel vs Time Graph?

​Calculate Avg Acceleration from:

1. 0s - 4 sec

2. 4 sec - 7 sec

3. 7 sec - 10 sec​

Poll

Acceleration is the change in velocity with time: True or False

• True

• False

​Acceleration Activity

​I'll jump off a chair but not the roof. Why?

​Avg. Acceleration & Instantaneous Acceleration

​How do I find the instantaneous acceleration at 5 seconds?

​How do I find the average acceleration between any two points?

Learning Objective

• To calculate the tangent of a curve

• To determine average and instantaneous acceleration from a velocity-time graph.

​To find Avg Accel between any two pts on the line, draw a straight line between those points and find the slope of the line.

​Instantaneous Acceleration is the acceleration at a specific point in time.

​

How do you propose to find out what the instantaneous acceleration is at 5 seconds?​

​To find Instantaneous Acceleration at a specific point in time (5 sec) we will draw a line tangent to the line at that point, then we will find the slope of that line.

Multiple Choice

A tangent touches the curve at more than one point: True or False

• True

• False

Multiple Choice

Using a tangent on a curve in velocity time graph we calculate the .............

• instantaneous acceleration

• av. acceleration

Multiple Choice

The formula for calculating avg acceleration is 

$$\frac{\left(v_f-v_i\right)}{t}$$  True or False

• True

• False

Multiple Choice

If the final velocity is greater than initial velocity, 

$$v_f>v_0$$  acceleration is

• positive

• negative

Multiple Choice

If the initial velocity is greater than final velocity, $$v_0>v_f$$   

acceleration is

• positive

• negative

​Just so you know.....

​

The area under the curve of the line of a velocity vs time graph, is displacement :)​

​

​Also..... a line tangent to a line at some point is called a derivative. That is the instantaneous rate of change at some pt. This is calculus.

​

​Also, the area under the curve of a linear function is called an Integral. This is also calculus.

​

Newton get really busy one year and invented it.​.. just for you. ;)

​Straight Lines - We can use Geometry

Curved Lines - This is where calculus comes in

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What does the slope of this graph represent?

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What does the slope of this graph represent?

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What does the area under the curve of this graph represent?

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What does the area under the curve of this graph represent?

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Calculate the distance travelled in section D

*Since this is speed vs time, the area under the curve is equal to distance (not displacement)

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Calculate the distance travelled in section C.

*Since this is speed vs time, the area under the curve is equal to distance (not displacement)