1. JEFFREY M. STA. INES, Ph.D. Instructor
MOTION
JEFFREY M. STA. INES, Ph.D.
Instructor

2. Acceleration of a car
Acceleration is the rate of change in the speed of an object.

3. Acceleration vs. Speed
Positive acceleration and positive speed

4. Acceleration vs. Speed
Negative acceleration and positive speed

5. Change in speed (m/sec)
4.1 Acceleration
Change in speed (m/sec)
Acceleration
(m/sec2)
a = Dv Dt
Change in time (sec)

6. 4.1 Calculate Acceleration
A student conducts an
acceleration experiment by coasting a bicycle down a steep hill.
The student records the speed of the bicycle every second for five seconds.
Calculate the acceleration of the bicycle.
1) You are asked for the acceleration.
2) You are given a table of speeds and times from an experiment.
3) a = (v2-v1) ÷ (t2 - t1)
4) Choose any two pairs of speed and time data.
a = (6 m/sec - 4 m/sec) ÷ (3 sec - 4 sec) = 2 m/sec2
For this experiment, the acceleration would have been the same for any two points.

7. Acceleration and Speed
Constant acceleration is different from constant speed.
Motion with zero acceleration appears as a straight horizontal line on a speed versus time graph.
zero acceleration
constant speed

8. Acceleration and Speed
Constant acceleration is sometimes called uniform acceleration.
A ball rolling down a straight ramp has constant acceleration.
constant acceleration
increasing speed

9. Acceleration and Speed
An object can have acceleration, but no speed.
Consider a ball rolling up a ramp.
As the ball slows down, eventually its speed becomes zero.
constant negative
acceleration
decreasing speed

10. Slope and Acceleration
Use slope to recognize when there is acceleration in speed vs. time graphs.
Level sections (A) on the graph show an acceleration of zero.
The highest acceleration (B) is the steepest slope on the graph.
Sections that slope down (C) show negative acceleration (slowing down).

11. A Model for Accelerated Motion
Key Question:
How do we describe and predict accelerated motion?

12. Slope of a graph
The slope of a graph is equal to the ratio of rise to run.
On the speed versus time graph, the rise and run have special meanings, as they did for the distance versus time graph.
The rise is the amount the speed changes.
The run is the amount the time changes.

13. Acceleration and slope
Acceleration is the change in speed over the change in time.
The slope of the speed versus time graph is the acceleration.

14. Calculate acceleration
The following graph shows the speed of a bicyclist going over a hill.
Calculate the maximum acceleration of the cyclist and say when in the trip it occurred.
1) You are asked for the acceleration.
2) You are given a graph of speed versus time.
3) a = slope of graph
4) The steepest slope is between 60 and 70 seconds, when the speed goes from 2 to 9 m/sec.
a = (9 m/sec - 2 m/sec) ÷ (10 sec) = 0.7 m/sec2

15. Acceleration
Is the time rate of change in velocity and can be computed :
a = ∆ V
∆ t
a= Vf-Vi
tf-ti

16. Sample problems
1. A jeepney has an initial speed of 30 m/s and its final speed is 40 m/s , if the time is 10 s compute for its acceleration

17. An object is given an acceleration of 6
An object is given an acceleration of 6.5 m/s2 the change of speed is 6 m/s. How long will it take the object to accelerate

18. 3. An automobile slows from 14. 0 m/s , East to 7. 0 m/s , East in 2
3. An automobile slows from 14.0 m/s , East to m/s , East in 2.0 s. Find its acceleration.
4. Starting from rest, a train acquired a speed 250 km/h during the time of 15 s. What is its acceleration

19. 5. A bus travels from Laguna to Manila with initial speed of 30 m/s after 5 seconds . Its speed become 60 m/s. What is its acceleration?