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

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

Acceleration vs. Speed Positive acceleration and positive speed

Acceleration vs. Speed Negative acceleration and positive speed

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

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.

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

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

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

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).

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

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.

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.

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

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

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

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

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 7.0 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

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?