CH 2: MOTION IN ONE DIMENSION

DISPLACEMENT AND VELOCITY

• Displacement-The length of the straight line drawn from your initial position to your final position as you move from one position to another• Change in position of an object• Measured in meters

• Displacement does NOT equal distance traveled

DISPLACEMENT AND VELOCITY

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DISPLACEMENT AND VELOCITY

• Displacement is an example of a quantity that has both direction and magnitude • In 1D motion there are only two directions in

which an object can move • These can be specified by plus and minus signs • Unless otherwise specified assume motion to the right is

positive and motion to the left is negative• Similarly upward motion will be considered positive and

downward displacement will be considered negative

DISPLACEMENT AND VELOCITY

• The choice of right as positive and left as negative is what is known as a convention

• Convention-is a system that is chosen for convenience and consistency, not necessarily because it has to be that way

• The convention can be reversed

DISPLACEMENT AND VELOCITY

• Velocity-The quantity that measures how fast something moves from one point to another• Has direction and magnitude

DISPLACEMENT AND VELOCITY

• To calculate the average velocity of an object you must know the objects • Displacement • Time the object left its initial position• Time the object arrived at its final position

Average velocity==

DISPLACEMENT AND VELOCITY

• Practice finding average velocity• During a race on level ground, Andra covers 825

m in 137 s while running due west. Find Andra’s average velocity

• If you left your house at 10 A.M. and arrived at your grandma’s house at 3 P.M. and your grandma’s house is 370 km to the west , What was your average velocity for the trip?

DISPLACEMENT AND VELOCITY

• The average velocity is equal to the constant velocity you would need to have to cover the given displacement in a given time interval

DISPLACEMENT AND VELOCITY

• In physics speed does NOT equal velocity• Velocity has direction and magnitude, speed only

has magnitude • Average velocity depends on the total

displacement• Average speed is equal to the distance traveled

divided by the time interval

DISPLACEMENT AND VELOCITY

• When graphing velocity graph time vs. position• The line connecting one point to another point

indicates the average velocity• The slope of the line connecting the first point to

the last point equals the average velocity• You can tell a lot about the velocity of an object

by the shape of its position-time graph

ACCELERATION

• Acceleration-the rate of change of velocity

• Calculated by dividing the total change in an object’s velocity by the time interval in which the change occurs

• Units m/s2

ACCELERATION

• Acceleration has direction and magnitude• When Δv is positive the acceleration is positive • When velocity is constant, the acceleration is

equal to zero • When something is slowing down the velocity is

positive, however, the acceleration is negative • A negative value for acceleration can also occur

when an object is moving in the negative direction and accelerating. This object decelerating would have a positive value

ACCELERATION

vi a Motion

+-

+-

Speeding upSpeeding up

+-

-+

Slowing downSlowing down

- Or +0

0- Or +

Constant velocitySpeeding up from rest

0 0 Remaining at rest

ACCELERATION

• Ball is fired with constant acceleration. A picture is taken every tenth of a second• Velocity increases by exactly the same amount

during each time interval • Displacement for each time interval increases by

the same amount

ACCELERATION

ACCELERATION

• A racing car reaches a speed of 4.2 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find how far the car moves while stopping.

ACCELERATION

• This equation can also help find the distance required for an object to reach a certain speed or to come to a stop

ACCELERATION

• A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8 m/s2 for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

ACCELERATION

• The square root of the right side of the equation must be taken to find the final velocity • The square root may be either positive or

negative, you must determine which is right • Table 2-4 contains the equations that are used

most often

ACCELERATION

• A babysitter pushing a stroller starts from rest and accelerates at a rate of 0.500 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?