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Chapter 3:

LINEAR MOTION

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Motion Is RelativeMotion of objects is always described as

relative to something else. For example:

• You walk on the road relative to Earth, but Earth is moving relative to the Sun.

• So your motion relative to the Sun is different from your motion relative to Earth.

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Speed

• Defined as the distance covered per amount of travel time (meters per second).

• In equation form:distance

Speed = time

Example: A girl runs 4 meters in 2 sec. Her speed is 2 m/s.

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Average Speed• The entire distance covered divided by the total

travel time– Doesn’t indicate various instantaneous speeds along

the way.

• In equation form:

total distance covered

Average speed time interval

Example: Drive a distance of 200 km in 2 h and your average speed is 100 km/h.

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Instantaneous Speed

Instantaneous speed is the speed at any instant.

Example: – When you ride in your car, you may speed up

and slow down. – Your instantaneous speed is given by your

speedometer.

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Velocity• A description of

– the instantaneous speed of the object– what direction the object is moving

• Velocity is a vector quantity. It has– magnitude: instantaneous speed– direction: direction of object’s motion– Average velocity = (initial vel + final vel )/ 2

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Speed and Velocity

• Constant speedspeed is steady speed, neither speeding up nor slowing down.

• Constant velocityvelocity is– constant speed and – constant direction (straight-line path with no

acceleration).

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Acceleration

Formulated by Galileo based on his experiments with inclined planes.

Rate at which velocity changes over time

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AccelerationInvolves a

• change in speed, or

• change in direction, or

• both.

Example: Car making a turn

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AccelerationIn equation form:

change in velocity

Acceleration time interval

Unit of acceleration is m/s2.

or

Final velocity – Initial velocity= Acceleration x time

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An automobile is accelerating when it isA. slowing down to a stop.

B. rounding a curve at a steady speed.

C. Both of the above.

D. Neither of the above.

AccelerationCHECK YOUR NEIGHBOR

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An automobile is accelerating when it isA. slowing down to a stop. B. rounding a curve at a steady speed.C. Both of the above.D. Neither of the above.

AccelerationCHECK YOUR ANSWER

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.

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Kinematic equations of motion:

• Vf = V0 +at

• Vf2 = V0

2 + 2aD

• D = V0t+0.5at2

• Note: – valid only if acceleration is constant.– If the object is in free fall; acceleration = g = 9.8 m/s2

– Note: The above equations will be provided during the test.

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Free Fall

Falling under the influence of gravity only - with no air resistance

• Freely falling objects on Earth accelerate at the rate of 9.8 m/s2.

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Free Fall—How Fast?The velocity acquired by an object starting from rest 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.

Velocity acceleration x time

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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.

Distance (1/2) x acceleration x time x time

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• The following are short problems which should give you ample exercise to get comfortable with problem solving. Also you can use these as a study guide for the test.

• Problem solving book: 10c, 11b, 16b & c, 24b &c, 26b &c. We will try to solve these (as many as possible) in class.

• If you are comfortable with the above, try the following at home: 38, 39, 42, 43, 45, 46, 51,55.(Most of these problems are very similar.)

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• Conceptual Physics textbook:

• Pg 46 – 7, 8, 10

• Pg 47 – 18, 21, 23

• Pg 49 – 5, 8, 17, 20, 27, 38, 40