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1.3 Acceleration

The Drop Tower at Canada’s Wonderland slowly carries you up in a seat to the top of the tower and then suddenly releases you!

On the way down, your arms and hair fly upward as the velocity of your seat increases. The thrill of this sudden change in motion can frighten and exhilarate you all at once.

Sudden changes in velocity are part of the thrill of theme park rides.

1.3 Acceleration

While it is true that objects sometimes move at constant velocity in everyday life,

usually the velocities we observe are not constant.

Recall that Non-Uniform Motion is motion that is not at a constant speed or in a

straight line.

- Acceleration () is the total change in velocity, divided by the total time elapsed. It is a vector quantity.
- SI units – metres per second, per second (squared) (m/s/s → m/s2).

- SP #2, 3 p.24, SP #1 p.25

1.3 Position-Time Graphs

- The position-time graph () of an accelerating object is curved.
Graph A

- The slope of the graph is increasing positive; object’s velocity is increasing [E].
- The object starts at rest at speeds up in the positive direction.

1.3 Position-Time Graphs

Graph B

- The slope of the graph is increasing negative; object’s velocity is increasing [W].
- The object starts at rest at speeds up in the negative direction.

1.3 Position-Time Graphs

Graph C

- The slope of the graph is decreasing positive; object’s velocity is decreasing [E].
- The object slows down in the positive direction and comes to a stop.

1.3 Position-Time Graphs

Graph D

- The slope of the graph is decreasing negative; object’s velocity is decreasing [W].
- The object slows down in the negative direction and comes to a stop.

1.3 Homework

- Practice # 2,3 p.24
- Practice # 1,2 p.25
- Questions #7-10 p.30

1.3 Velocity-Time Graphs (Part 2)

- A velocity-time graph () is a graph that describes the motion of an object, with velocityon the (vertical) y-axis, and time on the (horizontal) x-axis.

1.3 Velocity-Time Graphs

- The slope of a velocity-time graph gives the accelerationof the object.
- Acceleration for SPH 3U is always constant! (Uniform)
- graphs for uniform acceleration are always straight lines.
- If an object is moving with a constant velocity it will produce a horizontal line on a graph .

- SP #1 p.23
- Determine the skateboard’s acceleration.

1.3 Velocity-Time Graphs

- The area under a velocity-time graph () provides the displacement of an object.

- SP #1 p.26
- Determine the skateboard’s displacement after 10.0 s.

1.3 Velocity-Time Graphs

- SP #2 p.26
Determine the object’s displacement after a) 5.0 s, b) 10.0 s.

1.3 Average Velocity vs. Instantaneous Velocity

- The average velocityof an object is determined by finding its displacement over a time interval; a range of time.
- The instantaneous velocity of an object is its velocity at a specific instant in time.
- To find the instantaneous velocity of an object, we draw a tangent line on a position-time graph() at the particular instant in time required, and determine its slope.
- A tangent is a straight line that touches a curve at a single point, and extends in the same direction as the curve at that point.

1.3 Average Velocity vs. Instantaneous Velocity

- SP #1 p.28
Determine the object’s instantaneous velocity @ 2.0 s.

1.3 Homework (Part 2)

- Practice # 1b,2a p.29
- Questions #4-6,11 p.30

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