Describing Motion Chapter 2

Clear and precise description of motion Fig. 2.co Average speed Instantaneous speed Velocity Acceleration

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

Speed Unit Conversion Example: (2.1 p 20) Convert 90 kilometers per hour to (a) miles per hour, and (b) meters per second 1 mile = 1.609 km 1 km = 0.6214 miles 1 hour =60 minutes 1 minute =60 second

Average Speed Average speed from Kingman to Flagstaff (50mph) Average speed from Flagstaff to Phoenix (54mph) Fig. 2.02 Average speed from Kingman to Phoenix (52mph) Average speed is the rate at which distance is covered over time.

Instantaneous Speed The 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.

Velocity Velocity 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.

Example A car goes around a curve at constant speed. Is the car’s velocity changing?

Changing Velocity A force is required to change either the magnitude (speed) or the direction of the velocity. Fig. 2.06

Instantaneous Velocity Fig. 2.03 Instantaneous velocity is the velocity at the precise instant. Size - equal to instantaneous speed Direction - equal to the direction of motion at that instant.

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

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.

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.

Average Acceleration Fig. 2.02 A 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

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?

Graphing Motion Time Position 0 s 0 cm 5 s 4.1 cm 10 s 7.9 cm 15 s 12.1 cm 20 s 16.0 cm 25 s 30 s 35 s 18.0 cm To describe the car’s motion, we can note the car’s position every 5 seconds.

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. 2.14 What can this graph tell us? D, v, a The graph displays information in a more useful manner than a simple table.

Slope The slope at any point on the distance-versus-time graph represents the instantaneous velocity at that time. Fig. 2.14 Slope is change in vertical quantity divided by change in horizontal quantity. “rise over run” Steepness of slope, Zero slope , Negative slope

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)

Velocity-versus-time Graph Horizontal axis represent time, and the vertical axis represent velocity. Fig. 2.14 What can this graph tell us? D, v, a (How can we find the distance ?)

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

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?

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?

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

Acceleration-versus-time Graph Horizontal axis represent time, and the vertical axis represent acceleration. Fig. 2.14 What can this graph tell us?

What can this graph tell us? Example: 100-m Dash Fig. 2.14 What can this graph tell us?

Example (Q26 p 36). The velocity-versus-time graph of an object is shown. Is the acceleration of the object constant?

Uniform Acceleration Uniform 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.

Uniform Acceleration (continue) Zero initial velocity

Uniform Acceleration (continue) Non-zero initial velocity

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)?