Chapter 3: LINEAR MOTION Page 7

Standard: Students will be able to describe motion through an object’s position, speed, and direction.

Essential Question How are speed and velocity similar and how are they different, in describing the movement of an object?

Motion is Relative Even things that appear to be at rest move. When we discuss the motion of objects, we describe their motion relative to other objects A book that is at rest, relative to the table it lies on, is moving at about 30 kilometers per second relative to the sun. The space shuttle moves at 8 kilometers per second relative to Earth below. A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track. Unless stated otherwise, the speed of things in our environment are measured relative to the surface of Earth. *

Motion is Relative The racing cars in the Indy 500 move relative to the track. *

Motion Is Relative Motion of objects is always described as relative to something else. For example: Although you may be at rest relative to Earth’s surface, you’re moving about 100,000 km/h relative to the sun.

Speed How fast an object is moving Scalar quantity: quantity that can be described by magnitude without direction Units are any combination of units for distance and time, such as m/s, mph, km/h In equation form: Example: If a girl runs 4 meters in 2 seconds, her speed is 2 m/s.

Speed *

Instantaneous Speed A car does not always move at the same speed. You can tell the speed of the car at any instant by looking at the car’s speedometer. The speed at any instant in time is called the instantaneous speed. *

Instantaneous Speed The speedometer gives readings of instantaneous speed in both mi/h and km/h. *

Average Speed In a trip by car, the car will certainly not travel at the same speed all during the trip. The driver cares about the average speed for the trip as a whole.

Average Speed The entire distance covered divided by the total travel time The instantaneous speeds along the way may have been higher, or they may have been lower, than the average speed for the trip. In equation form: Example: Drive a distance of 200 km in 2 h and your average speed is 100 km/h.

Average Speed CHECK YOUR NEIGHBOR The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. 16

Average Speed CHECK YOUR ANSWER The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. Explanation: Average speed = total distance / time So, average speed = 30 km / 1 h = 30 km/h. Same Now, if we drive 60 km in 2 hours: Average speed = 60 km / 2 h = 30 km/h 17

Velocity A description of Velocity is a vector quantity. It has the instantaneous speed of the object AND what direction the object is moving Velocity is a vector quantity. It has magnitude: instantaneous speed direction: direction of object’s motion Example: An airplane moving North at 500 mph A missile moving towards you at 200 m/s

Question How are speed and velocity similar and how are they different, in describing the movement of an object? Draw a Venn diagram on the page opposite your notes Speed is just distance/time. Velocity includes direction as well.

Constant Speed and Velocity Constant speed is steady speed, neither speeding up nor slowing down. Constant velocity is constant speed AND constant direction (straight-line path with no acceleration).

Acceleration Rate at which velocity changes over time What happens to the speed of the red ball in each instance? Is each ball accelerating?

Acceleration In equation form: Unit of acceleration is unit of velocity divided by unit of time. Example: You car’s speed right now is 40 km/h. Your car’s speed 5 s later is 45 km/h. Your car’s change in speed is 45 – 40 = 5 km/h. Your car’s acceleration is 5 km/h/5 s = 1 km/h/s. 0 s 1 s 2 s 3 s 4 s

Acceleration Involves a change in speed, or change in direction, or both. Example: Car increasing or decreasing speed Car making a turn Car speeding up and turning

Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating

Acceleration CHECK YOUR NEIGHBOR An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. 26

Acceleration CHECK YOUR ANSWER An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. Explanation: Change in speed (increase or decrease) is acceleration, so slowing is acceleration. Change in direction is acceleration (even if speed stays the same), so rounding a curve is acceleration. Acceleration occurs due to a change in either speed or direction (or both). When a car slows down it changes its speed, so it is accelerating. When a car rounds a curve, although its speed is steady it is accelerating because it is changing direction. 27

Acceleration Steeper inclines have greater accelerations. When the incline is vertical, acceleration is at a maximum; same as that of the falling object. When air resistance is negligible, all objects fall with the same unchanging acceleration. 10 m/s2 (more precisely, 9.8 m/s2).

Free Fall motion under the influence of gravity only (no air resistance) free fall can occur only where there is no air in a vacuum or in space

Free Fall—How Fast? The velocity acquired by a falling object starting from rest (0 m/s) is So, under free fall, when acceleration is 10 m/s2, the speed is 10 m/s after 1 s. 20 m/s after 2 s. 30 m/s after 3 s. And so on.

Free Fall—How Fast? CHECK YOUR NEIGHBOR A free-falling object has a speed of 30 m/s at one instant. Exactly 1 s later its speed will be the same. 35 m/s. more than 35 m/s. 60 m/s. 31

Free Fall—How Fast? CHECK YOUR ANSWER A free-falling object has a speed of 30 m/s at one instant. Exactly 1 s later its speed will be the same. 35 m/s. more than 35 m/s. 60 m/s. The object gains 10m/s after every second. So, at a given instance, if its speed is 30m/s, then a second later it will be 10m/s greater than that i.e. 30m/s + 10m/s = 40m/s So, Its speed a second later is 40m/s which is more than 35m/s. Explanation: One second later its speed will be 40 m/s, which is more than 35 m/s. 32

Free Fall—How Far? The distance covered by an accelerating object starting from rest is So, under free fall, when acceleration is 10 m/s2, the distance is 5 m/s after 1 s. 20 m/s after 2 s. 45 m/s after 3 s. And so on.

Free Fall—How Far? CHECK YOUR NEIGHBOR What is the distance covered of a freely falling object starting from rest after 4 s? 4 m 16 m 40 m 80 m 34

Free Fall—How Far? CHECK YOUR ANSWER What is the distance covered of a freely falling object starting from rest after 4 s? 4 m 16 m 40 m 80 m Explanation: Distance = (1/2) x acceleration x time x time So: Distance = (1/2) x 10 m/s2 x 4 s x 4 s So: Distance = 80m 35