1. Aim: How do we analyze the area under velocity-time graphs?

2. Velocity-Time Graphs in Action
1) Does the red car pass the blue car at three seconds? If not, then when does the red car pass the blue car?
2) When lines on a velocity-time graph intersect, does it mean that the two cars are passing by each other? If not, what does it mean?

3. The meaning of the area under a curve in a velocity-time graph
Ideas?

4. Meaning of the Area under a curve
The area under a curve of a velocity-time graph is the displacement. When the area is negative, the displacement is negative. When the area is positive, the displacement is positive. The distance will always be positive.

5. Calculate the distance traveled in each of the examples given

6. Areas

7. Calculate the displacement of the following v-t graphs:
Problem A. What is the displacement of the object from t =2s to t =3s? Problem B. What is the displacement of the object from t = 0s to t = 2s?

8. Velocity-Time Graph
During what times will the displacement be negative? During what time interval will the displacement be positive?

9. V-t Graph and Superman
The velocity-time graph below pertains to the motion of Superman.
Calculate the acceleration at the following times: t=0-10s, t= 10s – 15s, , t=15s -40s, t= 40s – 55s
Calculate the distance travelled from t = 0s to t =15s.
Calculate the displacement of Superman at t =55s

10. Motorist
A motorcycle moves according to the velocity-versus-time graph shown in the figure. Find the average acceleration and distance travelled during each of the time segments A, B, and C.

11. Finding the average velocity
a) How do we find the average velocity of the object in the graph from t= 0s to t = 8s?
b) What is the average velocity of the object from t= 8s to t= 16s?

12. Free Response Practice Question 1
Question # 1- You will have to calculate acceleration.
A car traveling at a speed of 13 m/s accelerates uniformly to a speed of 25 meters per second in 5.0 seconds. Calculate the acceleration of the car during this 5.0 second interval. (Show all work, including the equation and substitution with units.)

13. Free Response Question 2
You will have to calculate average velocity. A truck moves at constant velocity and travels a distance of 190 meters in a 5.0 second time interval. Calculate the speed of the truck. (Show all work.)

14. Free Response Question 3

15. Free Response Question 3a-3c
a) Determine the magnitude of the acceleration of the Batman Mobile during the interval AB. (Show all work including equations and substitutions with units). b) Determine the distance travelled by the Batman Mobile during the interval BC. (Show all work including equations and substitutions with units). c) Determine the average speed of the Batman Mobile during interval CD.

16. Multiple Choice Question 1
1. Which is a vector quantity? a) Distance b) Mass c) Displacement d) Speed

17. Multiple Choice Question 2
A baseball player runs 27.4 meters from the batter’s box to first base, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player’s total displacement from the batter’s box is a) 3.0 m shorter (b) 3.0 m longer (c) 6.0 m shorter (d) 6.0 m longer

18. Multiple Choice Question 3
3. Which statement best describes the movement of an object with zero acceleration? a) The object must be at rest b) The object must be slowing down c) The object may be speeding up d) The object may be in motion

19. Multiple Choice Question 4
4. In a 4 km race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6.0 minutes. The average speed of the runner for the race is approximately a) 0.16 km/min b) 0.33 km/min c) 12 km/min d) 24 km/min

20. Multiple Choice Question 5
If an object is traveling east with a decreasing speed, the direction of the object’s acceleration is a) north b) south c) east d) west