Describing Motion Chapter 2
Clear and precise description of motion Average speed Instantaneous speed Velocity Acceleration
Speed • Speedis how fast something is moving. • Average speedis 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) 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 speedis 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.
A car goes around a curve at constant speed. Is the car’s velocity changing? Example
Changing Velocity A force is required to change either the magnitude (speed) or the direction of the velocity.
Instantaneous Velocity Instantaneous velocityis the velocity at the precise instant. Size - equal to instantaneous speed Direction - equal to the direction of motion at that instant.
Acceleration • Accelerationis 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). • Accelerationcan 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.) What is the direction of the acceleration? At the right angles to the velocity. • If a car goes around a curve at constant speed, is it accelerating? Why?
Average Acceleration 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 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 . 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 velocityat that time. • Slopeis 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. 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
(Q21 p 35). Example 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.
Acceleration-versus-time Graph Horizontal axis represent time, and the vertical axis represent acceleration. What can this graph tell us?
Example: 100-m Dash 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)?