1. Instantaneous Speed
Lesson 9
January 31st, 2011

2. Instantaneous speed The speed at a particular moment in time.
Speeds before and after that particular moment do not affect the instantaneous speed.

3. For any object moving at a constant speed, the instantaneous speed is the same at any time, and equals the constant speed. For an example of this, see the graph below
Δ d
Δ d
Δ t
Δ t

4. If the velocity is not consistent, the object has accelerated or decelerated. This causes a change in distance in each time interval.
The graph will not be a straight line but is often a smooth curve if the increase in speed is uniform, (uniform acceleration).
We cannot take the slope like we did previously as we will need a very small section of time and there is no straight line to follow.
Distance

5. Tangent Distance This is accomplished by drawing a Tangent.
A straight line that just touches the curve at one point, and represents the instantaneous slope at that one point along the curve.
Draw this
Distance
Δ d
Δ t

6. Calculating Instantaneous speed
Distance time graph
Instantaneous speed is the slope of a tangent to the curve at that moment.
Distance
Δ d
Δ t

7. Calculating Instantaneous speed
Speed Time graph
Instantaneous speed is read directly from the line on the graph for that moment.
speed

8. Average Speed
Average speed of a distance time graph is found by using the formula.

9. If the distance time graph is curved
If the distance time graph is curved. The average speed can still be found by drawing a straight line that connects the two ends of the curved line and then take the slope. Δd Δt

10. Questions
State in your own words, the meaning of constant speed, average speed, and instantaneous speed. C (3)
If a cat is running at a constant speed of 10km/h for 5 seconds, what is the average speed and what is its instantaneous speed at 4 seconds? T (1)
If the cat is walking at 2km/h and then accelerates constantly to a final speed of 14 km/h, what is the average speed over 10 seconds? T (1)
How is the instantaneous speed obtained from a speed-time graph? C (1)

11. 4. Instantaneous speed is the slope of a tangent to the curve on a distance time graph.
A. Show how it would be possible to use two or more tangents, at different points along the curve to calculate acceleration. C (1)
B. What error might there be in this situation? C (1)

12. 5. The performance of a mercury cougar is determined on a test track
5. The performance of a mercury cougar is determined on a test track. The carecovered a total of 402 m during the 16 second interval.
During which time interval(s) is the acceleration approximately consistent? (hint, use a ruler, some spots are straighter than it looks) T (1)
What is the instantaneous speed at 2 s, 8 s, and 14 s, T (1)
What is the average speed for the whole road test? (note, the acceleration is not constant throughout the test.) T(3) C (1)

13. 6. The graph below and to the right shows three different bicycle trips Labelled A, B, and C.
Which graph illustrates a constant speed for the whole trip? T (1)
Which graph shows a constantly changing speed? T (1)
Which graph(s) has (have) an instantaneous speed of zero at some point? T (1)
What is the instantaneous speed at 1.0 min for each graph? T (1)
Calculate the average speed for 0 to 5.0 min for each cyclist. T (3)