1. Motion in One Dimension
Chapter 2
Motion in One Dimension
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2. Herriman High AP Physics C
What is Mechanics
The study of how and why objects move is called Mechanics.
Mechanics is customarily divided into 2 parts kinematics and dynamics.
We will begin with the simplest part of kinematics – motion in a straight line. This is know as linear or translational motion.
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3. Descriptions of Motion
All motions are described in terms of a position function – X(t)
Motions can be described both graphically and mathematically and we will use both descriptions in describing motion in physics
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4. Describing Motion Three Common Situations
No motion
X(t) = A
Motion at a constant speed
X(t) = A + Bt
Accelerating Motion X(t) = A + Bt + Ct2
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5. Average Velocity If you divide distance by time you get average speed
Example: S = D/t = 500 miles/2 hours =250 mph
If you divide displacement by time you get average velocity
Example: Vavg = Δx/Δt = 500 miles North/2 hours = 250 mph North
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6. Instantaneous Velocity
Unlike average velocity which takes a mean value over a period of time, instantaneous velocity is the velocity function at a given instant, this is a derivative of the position function
V(t) = dx/dt
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7. Describing Instantaneous Velocity Three Common Situations
No motion
X(t) = A X = 5 m
V(t) = dx/dt = 0 m/s
Motion at a constant speed
X(t) = A + Bt = 5 + 3t
V(t) = dx/dt = 3 m/s
Accelerating Motion
X(t) = A + Bt + Ct2 = 5 + 3t + 4t2
V(t) = dx/dt = 3 + 4t m/s
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8. Herriman High AP Physics C
Average Acceleration
Acceleration is defined as the change in velocity with respect to time
a = Δv/t = (v2 – v1)/t
Δ – the greek symbol delta represents change
Example: If a car is traveling at 10 m/s and speeds up to 20 m/s in 2 seconds, acceleration is:
a = (20 m/s – 10 m/s)/2 seconds = 5 m/s2
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9. Describing Instantaneous Acceleration
Motion at a constant speed
V(t) = 3 m/s
A(t) = dv/dt = 0 m/s2
Accelerating Motion
V(t) = t m/s
A(t) = dv/dt = 4 m/s2
This is motion with a constant acceleration the most common case we will cover during this course
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10. Herriman High AP Physics C
Important Variables
x – displacement – measured in meters
v0 (Vnaught) – Initial Velocity – in m/s
vf (Vfinal) – Final Velocity – in m/s
a – acceleration – in m/s2
t – time – in seconds
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11. Motion with Constant Acceleration
Since a = (vf – v0)/t we can rearrange this to:
vf = v0 + at
and
since x = vavgt and
since vavg = (vf + v0)/2
A new equation is derrived:
x = v0t + ½ at2
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12. Motion with Constant Acceleration
Using this equation:
x = v0t + ½ at2
and since we can rearrange a previous equation:
vf = v0 + at to solve for time which gives us: t = (vf – v0)/a
Substituting the second into the first we get:
vf2 = v02 + 2ax
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13. Summary of the Kinematic Equations
Just a hint – Your “A” truly depends upon memorizing these and knowing how to use them!
Vavg = x/t
vavg = (vf + v0)/2
vf = v0 + at
x = v0t + ½ at2
vf2 = v02 + 2ax
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14. Problems Using the Kinematics
Acceleration of Cars
Braking distances
Falling Objects
Thrown Objects
Math Review – The Quadratic Equation
x = (-b± SQRT(b2-4ac))/2a
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