One Dimensional MotionReview of the basics

AP Physics

Terms

Displacement vs. Distance

Displacement: Change in position (vector)

Distance: How far an object has traveled (scalar)

Terms

Velocity vs. SpeedVelocity: Rate of the change in position

(vector)

Speed: Rate of distance covered (scalar)

Terms

Acceleration vs. Acceleration?Acceleration: The rate at which velocity

changes (vector) This could be a change in:

• Speed• Direction• Speed and direction

Position vs. Time Graph

The slope of

an x vs. t

graph is the

velocity

What are the velocities?

rise 2 0(a) 2 /

run 1 0(b) 0 m/s

(c) 1 m/s

0 3 3(d) 1.5 /

5 3 2

xm s

t

m s

Average Velocity on an x-t graph

Average velocity vs instantaneous velocity

on an position – time graph

As the two points P1 and P2 get closer, the time frame (∆t) gets smaller and smaller approaching zero. Eventually you are considering a moment in time rather than a period of time. Graphically, you are looking at the slope of a tangent line rather than the slope of the line connecting two points.

Instantaneous Velocity on an x-t graph

Velocity vs. Time Graph

The slope of a v vs. t graph is the acceleration

The area between the curve and the horizontal axis of a v vs. t graph is the displacement

Instantaneous Acceleration vs Average Acceleration from a v-t graph

As the two points P1 and P2 get closer, the time frame (∆t) gets smaller and smaller approaching zero. Eventually you are considering a moment in time rather than a period of time. Graphically, you are looking at the slope of a tangent line rather than the slope of the line connecting two points.

What are the accelerations and displacements?

2(A) a=2 m/s

1x=

2(.5)(5)(10) 25

bh

m

(B) a=0

x = LW

(10)(10) 100m

2(C) 0.5 /

1

2(5 10) (.5 10 5) 75

a m s

x LW bh

x x x m

Acceleration vs. Time Graph

The slope means NOTHING The area between the curve and the horizontal

axis is the change in velocity

a

t-10 m/s/s

10 s

100 /v m s

Important

Acceleration tells us how fast velocity changes

Velocity tells us how fast position changes

Falling Bodies, thrown up objects, and the y-direction

All things fall at the same rate (neglecting air resistance)

On earth that rate is 9.80 m/s2DOWNWATCH THE DIRECTION!The name of that acceleration is

Gravitational acceleration

Thanks!

This is a good quick review for kinematics. However, it is just a review not the end all be all of kinematics.