U
Unit 3: Kinematics
Uniform Rectilinear Motion
Uniform Accelerated Rectilinear Motion
The Motion of Projectiles
graphs: slope of a line
slope = rise/run
if y vs x then slope = Δy/Δx
If the graph is displacement versus time:
slope = Δd/Δt = d2 - d1/ t2 - t1 = velocity
If the graph is velocity versus time:
slope = Δv/Δt = v2 - v1/ t2 - t1 = acceleration
Uniform Motion:
Constant speed: an object moves equal distances in equal time intervals
Uniform Motion(: an object moves with constant velocity (constant speed and direction)
Graphs:
Velocity vs Time: uniform motion
v
t
remember constant velocity on a displacement vs time graph?
d
t
Acceleration
the change in velocity over time
a = Δv/Δt = m/s2
a truck's speed changes from 5 m/s to 50 m/s, in 60 seconds, what is its acceleration?
50m/s ­ 5m/s / 60s = 45/60 m/s2
= .75m/s2
Uniformly Accelerated Rectilinear Motion
velocity is no longer constant (more real)
velocity varies moment to moment
ti = initial time (s)
tf = final time (s)
xi = initial position (m)
xf = final position (m)
vi = initial velocity (m/s)
vf = final velcity (m/s)
a = acceleration (m/s2)
Instantaneous velocity
velocity at a precise moment in time
On a graph:
position versus time, if velocity is not constant, we
have a curve.
The velocity is the slope, but when the curve is
changing, what do we do?????
d
t
take the tangent of the curve
d
t
a=
y2 - y1
x2 - x1
velocity vs time graphs
v
t
There is a constant change in velocity, this object is speeding up with uniform acceleration
a = Δv/Δt = ?
p228­229
Notice how velocity is presented as a vector in question #7
They are directional, "east"(+) or "west" (-)
The length of the error is proportional to the spped.
Can a car have a positive acceleration and negative
direction?
Negative acceleration and positive direction?
Equations of Uniform Acceleration
Equation 1: a = Δv/Δt = v2 - v1/Δt
a * Δt = v2 - v1
a * Δt + v1 = v2
Equation 1:
v2 = v1 + at
Equation 2: xf = xi + ½(vi + vf)Δt
Equation 3: xf =xi + v1t + ½at2
Equation 4: vf2 = vi2 + 2aΔx
How to solve kinematic problems:
textbox p232
• draw a diagram
• origin of x axis, at starting point, xi = 0
• id ti and tf
• id known parameters (be sure to indicate
signs (+ or -)
• Find one of the 4 equations where the
quantity sought is the only unknown
Example:
The driver of a car which is moving
east at 25m/s applies the brakes
and begins to decelerat at 2.0m/s2
How far does the car travel in
8.0s?
a = -2.0 m/s2
vi = 25 m/s
t = 8.0 s
d=?
which formula?
d = vit + 1/2 a t2
d = 25(8.0) + 1/2(-2.0)(8.02)
d = 200 - 64
d = 136 m (+)
Examples in text book p 232
A:
B:
Practice: Section 10.2
p. 234
p. 234
1. What do we know?
Δd = 402m vi= 0m/s
Δt = 6.0s xi = 0m xf = 402m
?a
? vf (km/h)
Look for formulas with only one
unknown....
xf = xi + (viΔt + 1/2(aΔt2))
find a
402 = 0 + (0*6 + 1/2(a*6^2)
402 = 1/2(a*36)
804 = 36a
a = 22.3m/s2 = 22m/s2
vf
vf2 = vi2 +2aΔx
vf2 = 0 + 2* 22.3 * 402
vf = √17929.2
vf = 133.9 m/s = 130 m/s
old text book
p. 213 1
p217
p. 220-222