CHAPTER 3 ACCELERATED MOTION   In this chapter you will:  Develop descriptions of accelerated motions. Use graphs and equations to solve problems involving moving objects. Describe the motion of objects in free fall.

CHAPTER 3 SECTIONS Section 3.1: Acceleration Section 3.2: Motion with Constant Acceleration Section 3.3: Free Fall

SECTION 3.1 ACCELERATION Objectives Define acceleration. Relate velocity and acceleration to the motion of an object. Create velocity-time graphs.

INTRO/CHANGING VELOCITY In this chapter we will be presented with situations in which the velocity of an object changes, while the object’s motion is still along a straight line. The most important thing to notice in these motion diagrams is the distance between successive positions.   If an object speeds up each subsequent velocity vector is longer. If an object slows down each subsequent velocity vector is shorter.

VELOCITY TIME GRAPHS Velocity Time Graph – a graph that can be used to plot the velocity of an object versus the time and it determines the sign of the object’s acceleration. The area under the curve of a Velocity Time graph is the DISPLACEMENT. The slope is the ACCELERATION. The rate at which the car’s velocity is changing can be found by calculating the slope of the velocity time graph.   Acceleration – the rate at which an object’s velocity changes. It is the velocity of an object divided by the time interval. It is measured in m/s2. It is the slope of a Velocity Time Graph. a = v/t

AVERAGE &INSTANTANEOUS ACCELERATION Average Acceleration – the change in velocity divided by that time interval. It is a vector quantity. It is measured in m/s2. a = vf – vi = v Average Acceleration Equation tf – ti t   When the velocity increases its change is positive and the Acceleration is Positive. When the velocity decreases its change is Negative and so is the Acceleration. Instantaneous Acceleration – the change in an object’s velocity at a specific instant in time. It is the slope of the tangent line at a specific instant of time.

DISPLAYING ACCELERATION ON A MOTION DIAGRAM Example 1 p. 60 Velocity: the runner’s velocity increased from 0 to 10 m/s in 4 s and then it almost levels off but slightly increases from 4 to 10 s. Acceleration: the runner accelerates in the first 4 s and then runs with almost a constant speed from 4 to 10 s. Also a = Rise / Run = (11 – 2.8) / (2.4 – 0) = 8.2 / 2.4 = a = 3.42 m/s2 And a = Rise / Run = (10.3 – 10) / (10 – 0) = .3 / 10 = a = .03 m/s2 Do Practice Problems p. 61 # 1-5

POSITIVE AND NEGATIVE ACCELERATION In other words, when the object’s acceleration is in the same direction as its velocity, the object’s speed increases. When they are in opposite directions the speed decreases.   Both the direction of an object’s velocity and its direction of acceleration are needed to determine whether it is speeding up or slowing down. The sign of acceleration does not indicate whether the object is speeding up or slowing down.

DETERMINING ACCELERATION FROM A V-T GRAPH Go Over Figure 3.8 a = vf – vi = v tf – ti t    Do Example Problem 2 p. 63 a = (0 – 2.5) / (5 – 0) = -2.5 / 5 = - .5 m/s2 So the sign is NEGATIVE as it rolls up the hill and the magnitude is .5 m/s2.   Do Practice Problems p. 64 # 6-11 Do 3.1 Section Review p. 64 # 12-17