2 Clear and precise description of motion Fig. 2.coAverage speedInstantaneous speedVelocityAcceleration
3 Speed Units of speed: MPH, km/hr, m/s, etc Speed is how fast something is moving.Average speed is total distance divided by the time of travel.Units of speed: MPH, km/hr, m/s, etc
4 Speed Unit ConversionExample: (2.1 p 20) Convert 90 kilometers per hour to (a) miles per hour, and (b) meters per second 1 mile = km 1 km = miles 1 hour =60 minutes 1 minute =60 second
5 Average SpeedAverage speed fromKingman to Flagstaff(50mph)Average speed fromFlagstaff to Phoenix(54mph)Fig. 2.02Average speed fromKingman to Phoenix(52mph)Average speed is the rate at which distance is covered over time.
6 Instantaneous SpeedThe speedometer tells us how fast we are going at a given instant in time.Instantaneous speed is the speed at that precise instant in time.It can be calculated as the average speed over a short enough time that the speed does not change much.
7 VelocityVelocity involves both the direction of the motion and how fast the object is moving.Velocity is a vector .Velocity has a magnitude (the speed) and also a direction of motion.A change in velocity can be a change in either the object’s speed or the direction of motion.
8 ExampleA car goes around a curve at constant speed. Is the car’s velocity changing?
9 Changing VelocityA force is required to change either the magnitude (speed) or the direction of the velocity.Fig. 2.06
10 Instantaneous Velocity Fig. 2.03Instantaneous velocity is the velocity at the precise instant.Size - equal to instantaneous speedDirection - equal to the direction of motion at that instant.
11 Acceleration Average acceleration and instantaneous acceleration Acceleration is the rate at which velocity changes.Acceleration can be either a change in the object’s speed or a change in the direction of motion (it is a vector).Acceleration can be either positive or negative.Average acceleration and instantaneous acceleration
12 Acceleration (cont.)The direction of the acceleration vector is that of the change in velocity, ∆v.If velocity is increasing (decreasing), the acceleration is in the same (opposite) direction as the velocity.
13 Acceleration (cont.)If a car goes around a curve at constant speed, is it accelerating? Why?What is the direction of the acceleration? At the right angles to the velocity.
14 Average AccelerationFig. 2.02A car starting from rest, accelerates to a velocity of 20 m/s due east in a time of 5 s. What is it average acceleration?Acceleration Units: velocity divided by time
15 Exercises (p 36):E2.9 A car travels with an average speed of 58MPH. What is the speed in km/h? (1 mile=1.61 km) E2.11 Starting from rest, a car accelerates at a rate of 4.2 m/s/s for a time of 5 seconds. What is the velocity at the end of this time?
16 Graphing MotionTimePosition0 s0 cm5 s4.1 cm10 s7.9 cm15 s12.1 cm20 s16.0 cm25 s30 s35 s18.0 cmTo describe the car’s motion, we can note the car’s position every 5 seconds.
17 Distance-versus-time Graph We can graph the data in the table, let the horizontal axis represent time, and the vertical axis represent distance .Fig. 2.14What can this graph tell us? D, v, aThe graph displays information in a more useful manner than a simple table.
18 SlopeThe slope at any point on the distance-versus-time graph represents the instantaneous velocity at that time.Fig. 2.14Slope is change in vertical quantity divided by change in horizontal quantity.“rise over run”Steepness of slope, Zero slope , Negative slope
19 A car moves a long a straight line so that its position varies with time as described by the graph here. A. Does the car ever go backward? B. Is the instantaneous velocity at point A greater or less than that at point B?Example (Q19, p35)
20 Velocity-versus-time Graph Horizontal axis represent time, and the vertical axis represent velocity.Fig. 2.14What can this graph tell us?D, v, a(How can we find the distance ?)
21 Example (Q18, p 35)In the graph shown here, velocity is plotted as a function of time for an object traveling in a straight line.Is the velocity constant during any time interval shown?During which time interval is the acceleration greatest?The slope of the velocity-versus-time graph is the acceleration
22 Example(Q21 p 35).A car moves along a straight section of road so its velocity varies with time as shown in the graph.Does the car ever go backward?At which point of the graph, is the magnitude of the acceleration the greatest?
23 Example(Q22 p 35).A car moves along a straight section of road so its velocity varies with time as shown in the graph.In which of the equal time segments, 0-2 seconds, 2-4 seconds, or 4-6 seconds, is the distance traveled by the car the greatest?
24 Example: a car traveling on a local highway A steep slope indicates a rapid change in velocity (or speed), and thus a large acceleration.A horizontal line has zero slope and represents zero acceleration.Fig. 2.14
25 Acceleration-versus-time Graph Horizontal axis represent time, and the vertical axis represent acceleration.Fig. 2.14What can this graph tell us?
26 What can this graph tell us? Example: 100-m DashFig. 2.14What can this graph tell us?
27 Example(Q26 p 36).The velocity-versus-time graph of an object is shown. Is the acceleration of the object constant?
28 Uniform AccelerationUniform Acceleration: The acceleration is constant.It is the simplest form of acceleration.It occurs when a constant force acts on an object.Most of the examples we consider will involve constant acceleration.Falling object.A car accelerating at a constant rate.
29 Uniform Acceleration (continue) Zero initial velocity
31 Example (SP2, p37) The velocity of a car increases with time as shown. What is the average acceleration between 0 s and 4 s?What is the average acceleration between 4 s and 8 s?What is the average acceleration between 0 s and 8 s?Is the result in (c) equal to the average of the two values in (a) and (b)?