A.
Kinematics in One Dimension
 Mechanics
– how &
why objects move
 Kinematics: the
description of how
objects move
a.
b.
Distance: total length of travel
Displacement: change in position
Let’s say a runner jogs a lap around a 100-meter
track. He returns back to where he started in
4 minutes.
a. What distance did he travel?
b. What was his displacement?
Our Very First Formula! Isn’t this exciting?
Displacement:

Δx = xf – xi ,
Where Δx = change in position, or displacement,
xf = final position, and
xi = initial position
*Displacement is directionally dependent! You CAN
have negative displacement!
 Use
a visual!
 Does
the odometer in your car measure
distance or displacement?
 Can
you think of a situation where it would
measure both?
A
particle moves from x = 1.0 m to x = -1.0 m.
What is the distance? Displacement?
 You
are driving around a circular track with a
diameter of 40 m. You drive around 2 ½ times.
How far have you driven? What is your
displacement?
Speed & Velocity
a.
Average Speed = distance traveled / elapsed
time of travel
Units: m/s
*Directionally Independent – always positive!
 You
nose out another runner to win the
100.000 m dash. If your total time for the race
was 11.800 s and you aced out the other
runner by 0.001 s, by how many meters did
you win?
 Velocity:
speed AND direction
 Velocity
= displacement/elapsed time
 Units: m/s

Directionally DEPENDENT! Pick your frame of reference –
which way is positive & which is negative?

Your friend Marsha lives 0.55km east of your
house. The nearest grocery store is 0.82km
west of your house. You walk from your
house to the grocery store for some soda. It
takes you 17 minutes to get there, and you
spend 3 minutes in the store. Then, in 12
minutes, you walk from the grocery store
over to Marsha’s house. Find the distance
you traveled, your displacement, your
average speed, and your average velocity.
 Graph
position vs. time for your trip to the
grocery store & Marsha’s house.
 The
slope of the line along each interval shows
your velocity!
Describe the object’s motion along each interval.


Instantaneous velocity is an object’s speed at a
point in time.
On a position vs. time graph, it equals the slope
of the tangent line at any time.
t(s)
x(m)
0
0
0.25
9.85
0.50
17.2
0.75
22.3
1.00
25.6
1.25
27.4
1.50
28.1
1.75
28.0
2.00
27.4
Acceleration

a.
b.
Review: v=Δd/Δt
Acceleration: how quickly an object’s velocity
changes
Acceleration can be:
a. Speeding up (v and a are in same direction)
b. Slowing down (different sign for v and a)
c.
Changing direction (2-D motion)
 Units

for acceleration are m/s2
In Physics B, we assume acceleration is constant.
 Saab
advertises a car that goes from 0 to 60.0
mi/h in 6.2s. What is the average acceleration
of this car?
 An
airplane has an average acceleration of 5.6
m/s2 during takeoff. How long does it take for
the plane to reach a speed of 150 mi/h?


Instantaneous acceleration can be found by
calculating the slope of the tangent line at a
point on a velocity vs. time graph.
Constant acceleration (in an ideal world):
instantaneous a = average a
Kinematic Equations

A car slows down along the road from 40.0
km/h to 24.0 km/h in just 3.70 seconds.
What is the car’s acceleration?

A ball is thrown into the air at a velocity of
15.0 m/s. It is caught at the same height
when it is traveling downward at a speed of
15.0 m/s. Find the average velocity of the
ball.
A
ball is dropped (not thrown) from a height of
77.2m. How long does it take to hit the
ground below? (neglect air resistance and
remember gravitational acceleration=
9.81m/s2)
 A skydiver is falling at a velocity of 8.2 m/s
downward. The parachute is opened, and
after falling 19m, the skydiver is falling at a
rate of 2.7m/s. What deceleration did the
parachute provide?
1. A child slides down a hill on a sled with an
acceleration of 1.5 m/s2. If she starts at rest,
how far has she traveled in (a) 1.0s, (b) 2.0s,
and (c) 3.0s?
2. On a ride at an
amusement park,
passengers accelerate
straight downward from
zero to 45mi/h in 2.2s.
What is the average
acceleration of
passengers on this ride?
4. Two cars drive on a straight highway. At time t=0,
car 1 passes mile marker 0 traveling due east with a
speed of 20.0 m/s. At the same time, car 2 is 1.0 km
east of mile marker 0 traveling at 30.0 m/s due west.
Car 1 is speeding up with an acceleration of
magnitude 2.5 m/s2, and car 2 is slowing down with
an acceleration of magnitude 3.2 m/s2. Write xversus-t equations of motion for both cars.
5. You’re driving around town at 12.0 m/s when
a kid runs out in front of your car. You brake –
your car decelerates at 3.5 m/s/s.
(a) How far do you travel before stopping?
(b) When you have traveled half that distance,
what is your speed?
(c) How much time does it take to stop?
(d) After braking half that time, what is your
speed?
Objects of different masses/weights fall with
the SAME ACCELERATION
(at sea level & neglecting air resistance)
b. What acts on an object in free fall?
-NOTHING but gravity (hence the free)
a.
c. Objects in free fall can move down, OR up!
d. g = 9.81 m/s/s ← g is always positive 9.81
m/s/s. If your frame of reference says
down is negative, use –g.
*If down is positive and x0=0, then x=1/2 gt2
(derived from that super-important eqn)
 At
what acceleration
does a 5000kg elephant
fall?
 What about a mouse?
 You
drop a ball from a 120-m high cliff
• How long is it in the air?
• What is its speed just before it hits the ground? (at
x=0m)
• Sketch x vs t, v vs t, and a vs t graphs for this