herriman high ap physics c chapter 2 motion in one dimension
TRANSCRIPT
Herriman High AP Physics C
Chapter 2
Motion in One Dimension
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.
Herriman High AP Physics C
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
Herriman High AP Physics C
Describing MotionThree 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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Herriman High AP Physics C
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
Herriman High AP Physics C
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
Herriman High AP Physics C
Describing Instantaneous Velocity
Three Common Situations No motion X(t) = A X = 5 mV(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
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
Herriman High AP Physics C
Describing Instantaneous Acceleration
Motion at a constant speed V(t) = 3 m/s
A(t) = dv/dt = 0 m/s2
Accelerating Motion V(t) = 3 + 4t 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
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
Herriman High AP Physics C
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
Herriman High AP Physics C
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:vf
2 = v02 + 2ax
Herriman High AP Physics C
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 = v0
2 + 2ax
Herriman High AP Physics C
Problems Using the Kinematics
Acceleration of Cars Braking distances Falling Objects Thrown Objects
Math Review – The Quadratic Equation x = (-b± SQRT(b2-4ac))/2a