Section 1: Measuring Motion
• Motion is observed when an object appears to change position relative to a reference point (frame of reference).
• The earth is the most common reference point.
• When an object changes position over time relative to a reference point, as you see in figure 1 page 118, the object is in motion .
• Speed is the distance traveled by an object divided by the time taken to travel that distance.
• The SI unit for speed is meters per second
(m/s). Other common units for speed are kilometers per second (km/s), feet per second (ft/s), and miles per hour (mi/h).
• Most of the time, objects do not move at a constant speed.
• Average speed is calculated using the following formula:
Average speed = total distance total time
• The formula for distance is speed • time.
• The formula for time is distance/speed.
• Speed can be represented on a distance-time graph. Time is on the x-axis, distance is on the yaxis.
• The slope of the line on a distance-time graph for speed represents the rate of speed.
• The steeper the slope, the greater the rate of speed.
• If the line is straight, the speed is zero.
• Draw a simple distance-time graph for the following: high rate of speed, low rate of speed, and a speed of zero.
Figure 2, page 119 : This figure shows a graph of the speed of a car over a four hour period.
• How far did the car actually travel in 2 hours?
•
200 km
• How far did the car travel in 4 hours?
•
360 km
• What was the average speed of the car?
• 90 km/h
• Try the practice problems in the Math Focus sections of page 120.
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Velocity is the speed of an object in a given direction.
• An example of velocity would be an airplane traveling 600 km/h south.
• An object’s velocity is constant only if its speed and direction are constant.
• Constant velocity is always motion along a straight line.
• Velocity is represented using an arrow. The point of the arrow shows the direction. The length of the arrow shows how much.
• Combining velocities of objects will determine resultant velocity .
• When combining velocities in the same direction, add them together.
• When combining velocities in opposite directions, subtract the smaller velocity from the larger velocity. The direction is the same as the larger.
• Figure 4 shows a person walking along the aisle of a bus while the bus is in motion.
• The resultant velocity of the person in the first illustration is 16 m/s east.
• The resultant velocity of the person in the second illustration is 14 m/s east.
• Why are these two velocities different?
•
Acceleration is the rate at which velocity changes over time.
• Remember: velocity involves both speed and direction.
• An object accelerates if either speed or direction change.
• The faster the velocity changes the greater the accleration.
• Acceleration is commonly associated with an increase in speed, but an object accelerates if it slows down as well. (refer to the definition of acceleration)
• An increase in velocity is called positive acceleration.
( This is the same as speeding up in the positive direction or slowing down in the negative direction.)
• A decrease in velocity is called negative acceleration. ( This is the same as slowing down in the positive direction or speeding up in the negative direction.)
• Acceleration is found by using the following formula:
A = final velocity – initial velocity time
• Try the Math Practice question on page
122.
• On a distance-time graph, acceleration is represented using a curved line.
• Some common units for acceleration are meters per second per second (m/s/s or m/s 2 ) or kilometers per hour per second
(km/h/s).
• Using algebra, rewrite the formula for acceleration to solve for final velocity.
– v f
= at + v i
• With circular motion, only the direction is changing, not the speed.
•
Centripetal acceleration is the acceleration that occurs in circular motion and is directed toward the center of the circular path.