1. Speed and Velocity Speed and Velocity
What is Speed, Velocity and Acceleration?
Speed and Velocity
(Use with Speed, Velocity and Acceleration handout)

2. Speed is the distance traveled per unit time.

3. Pretend you are looking at your car's speedometer while you are driving. The reading you get from your speedometer is
instantaneous speed…
This is the speed that you are traveling at that moment.

4. Average speed is the distance traveled divided by the time
Average speed is the distance traveled divided by the time. It can be calculated using the following formula:
speed =
distance
time
...or shortened:
s = d t

5. Four Step Approach to solving problems
Step 1 Read the problem, draw a picture
Step 2 Write down what you know, What are you trying to find?
Step 3 Set up the formula
Step 4 Plug in the numbers Solve

6. “A car traveled 110 miles in 2 hours”
Consider the problem…
“A car traveled 110 miles in 2 hours”
Step 1 Read the problem, draw a picture
110 miles
2 hours
Formula
Plug-in
Answer
d =
t =
s =
Units, units, units!

7. ? “A car traveled 110 miles in 2 hours” 110 miles 2 hours Formula
Step 2 Write down what you know, What are you trying to find?
110 miles
2 hours
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours
s = ?
Units, units, units!

8. ? “A car traveled 110 miles in 2 hours” s = d t Formula Plug-in Answer
Step 3 Set up the formula
s = d t
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours
s = ?
Units, units, units!

9. ? “A car traveled 110 miles in 2 hours” Formula Plug-in Answer d =
Step 3 Set up the formula
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours d
S =
s = ? t
Units, units, units!

10. “A car traveled 110 miles in 2 hours”
Step 4 Plug in the numbers and Solve 55
mi/hr
Formula
Plug-in
Answer
d =
110 mi
2 hours
t = d
110 mi
S =
S =
S = 55
mi/hr
s = 55
mi/hr t
2 hr
Units, units, units!

11. Do the problems 1-3 on your notes

12. Consider the problem…
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 1 Read the problem, draw a picture
Speed of runner: 20 km/hr
10 km
Formula
Plug-in
Answer
d =
t =
s =
Units, units, units!

13. “A runner’s average speed during the 10 kilometer race was 20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 2 Write down what you know, What are you trying to find?
Speed of runner: 20 km/hr
10 km
Formula
Plug-in
Answer
d =
10 km
t = ?
s =
20 km/hr
Units, units, units!

14. “A runner’s average speed during the 10 kilometer race was 20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 3 Set up the formula
s = d t
Formula
Plug-in
Answer
d =
10 km
s (km/hr) =
d (km)
t (hr)
t = ?
s =
20 km/hr
Units, units, units!

15. Cross multiply and divide…
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 4 Plug in the numbers and Solve
Time: 0.5 Hour
Formula
Plug-in
Answer
d =
10 km
.5 hr
20 km
10 km
t =
S = d t =
10 km =
.5 hr
1 Hr (t)
t (hr)
20 km x t (hr)
s =
20 km/hr
Proportion Problem…
Cross multiply and divide…
Units, units, units!

16. Do the problems 4-5 on your notes

17. “You decide to go to Dallas to see friends
“You decide to go to Dallas to see friends. Your friends tell you that it takes 4 hours to get to Dallas at an average speed of 70 miles per hour. Approximately ho many miles is it to their house.”
4 hours
70 miles per hour
Step 1 Read the problem, draw a picture
Step 2 Write down what you know, What are you trying to find? ?
Step 3 Set up the formula
Step 4 Plug in the numbers and Solve
Formula
Plug-in
Answer
d =
280 mi
4 hr
t =
s = d / t
70mi x 4hr
70 mi
1 hr =
d (mi)
4 hr =
280 mi
d x 1hr
s =
70 mi/hr
70 mi/hr = d/4 hr
Units, units, units!

18. Do the problem 6 on your notes

19. instantaneous speed (speed on your speedometer) and average speed do not involve direction.

20. What is the difference between speed and velocity?
55 mi/hr
Velocity has speed & direction.
55 mi/hr
All of these cars had different velocities because they were going in different directions
55 mi/hr

21. A distance Time graph makes it possible to “see” speed.
This graph shows how fast the swimmers went during their workout.
Which swimmer went and a constant (the same) speed throughout her workout?
Constant speed
Is a straight line
Which one stopped during their workout?
Stopped here
400 meters at 10, 15, & 20 minutes

22. Make the Speed graph
& Answer the questions

23. Acceleration

24. Acceleration is defined as the change in velocity over time.
final velocity – initial velocity
time
acceleration =
Vf - Vi t
a =

25. A go-cart started at the top of a hill at 5 meters per second and ended up at the bottom of the hill at 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Step 1 Read the problem, draw a picture
5 m/s
top
Vf =
In 6 s
Formula
Plug-in
Answer
Vi=
t =
a =
bottom
35 m/s

26. A go-cart started at the top of a hill at 5 meters per second and ended up at the bottom of the hill at 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
5 meters
per second
35 meters per second
6 seconds
Start:
initial Velocity
Step 2 Write down what you know, What are you trying to find?
5 m/s
top
final velocity – initial velocity
acceleration =
time
Vf =
35 m/s
6 s
Formula
Plug-in
Answer
Vi=
5 m/s
t =
6 s
a = ?
bottom
Finish:
final Velocity
35 m/s

27. A go-cart started at the top of a hill at 5 meters per second and ended up at the bottom of the hill at 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Initial Velocity
Step 3 Set up the formula Cover what you don’t know
5 m/s
top
Vf - Vi t
Vf =
35 m/s
Formula
Plug-in
Answer
6 s
Vi=
5 m/s
Vf - Vi t
t =
6 s
a = ?
bottom
35 m/s
Final Velocity

28. Step 4 Plug in the numbers and Solve
A go-cart started at the top of a hill at 5 meters per second and ended up at the bottom of the hill at 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Step 4 Plug in the numbers and Solve
Vf =
35 m/s
Formula
Plug-in
Answer
Vi=
5 m/s
Vf - Vi
35m/s – 5 m/s
30 m/s =
5 m/s2
t =
6 s t 6s
6 s
a =
5 m/s2

29. Do the problems 8-9 on your notes

30. Acceleration is defined as the change in velocity over time.
Any time an object's velocity is changing, we say that the object is accelerating.
This brings up an important point. In common language, when things speed up, we say that they are "accelerating", and, when they slow down, we say that they are "decelerating".

31. However, in the language of physics, we say that both objects are accelerating, not because both objects are speeding up, but because both objects have changing velocities.

32. 70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h
Velocity involves both speed and direction. Changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction.
70 mi/h
70 mi/h
70 mi/h

33. Consider a car moving at a constant speed of 55mph while turning in a circle. The car's velocity is not constant, even though the speed is constant. This is because the direction of motion is constantly changing while the car is turning. Since the direction is changing, even though the speed is not, the velocity is changing. (velocity involves both speed and direction.) As a result, the car is accelerating, even though it is neither speeding up or slowing down. The car is accelerating because its velocity is changing.