Physics 121
2. Motion in one Dimension
2.1 Reference Frames and Displacement
2.2 Average Velocity
2.3 Instantaneous Velocity
2.4 Acceleration
2.5 Motion at Constant Acceleration
2.6 How to Solve Problems
2.7 Falling Objects
2.8 Graphs of Linear Motion
Speed
Speed = Distance / Time
v=d/t
Example 2.1 . . . From a Distance
If you are driving 110 km/h along a straight
road and you look to the side for 2.0 s, how far
do you travel during this inattentive period?
Solution 2.1 . . . From a Distance
Given: v = 110 km/h
t = 2.0 s
Solve for: d
Formula v = d/t
But first … convert speed (v) into m/s!!!
110 km/h = 110 km/h x 1000 m/km / 3600 s/h
110 km/h = 30.6 m/s
v = d/t
30.6 m/s = d / 2.0 s
d = 30.6 m/s x 2.0 s
d = 61 m
Distance and Displacement
Displacement measures the change in position
of an object. Also, the direction, in addition to
the magnitude, must be considered.
Distance and Displacement can be very
different if the object does not proceed in the
same direction in a straight line!
Example 2.2 . . . Around the block
A car travels East from point A to point B (5
miles) and then back (West) from point B to
point C (2 miles).
(a) What distance did the car travel?
(b) What is the car’s displacement?
A
C
B
Solution 2.2 . . . Around the block
A car travels East from point A to point B (5
miles) and then back (West) from point B to
point C (2 miles).
(a) Distance traveled is 7 miles
(b) Displacement is 3 miles East
A
C
B
Speed and Velocity
Velocity = displacement / time
•Car A going at 30 m.p.h. EAST and car B
going at 30 m.p.h. NORTH have the same
speed but different velocities!
•A car going around a circular track at 30
m.p.h. has a CONSTANT SPEED but its
VELOCITY is CHANGING!
Example 2.3 . . . Speed and Velocity
John Denver negotiates his rusty (but trusty) truck around
a bend in a country road in West Virginia.
A. His speed is constant but his velocity is changing
B. His velocity is constant but his speed is changing
C. Both his speed and velocity are changing
D. His velocity is definitely changing but his speed may or
may not be changing
Solution 2.3 . . . Speed and Velocity
John Denver negotiates his rusty (but trusty) truck around
a bend in a country road in West Virginia.
A. His speed is constant but his velocity is changing
B. His velocity is constant but his speed is changing
C. Both his speed and velocity are changing
D. His velocity is definitely changing but his speed may or
may not be changing
Example 2.4 . . . On the road again!
A car travels East from point A to point B (5
miles) and then back (West) from point B to
point C (2 miles) in 15 minutes
(a) What is the speed of the car?
(b) What is velocity of the car?
A
C
B
Solution 2.4 . . . On the road again!
A car travels East from point A to point B (5
miles) and then back (West) from point B to
point C (2 miles).
(a) Speed is 28 mph
(b) Velocity is 12 mph East
A
C
B
Instantaneous Velocity
• Instantaneous means measured at a given instant
or moment (“Kodak moment”). Experimentally,
this is virtually impossible. One must measure
the distance over an extremely short time interval
• Average means measured over an extended time
interval. This is easier to measure.
Speed and Velocity . . . revisited!
• Speed = distance / time
• Velocity = displacement / time
• For translational motion (straight line) in the same
•
•
direction, speed equals velocity!
Speed is an example of a SCALAR quantity. Only the
magnitude (amount) is specified without regard to the
direction
Remember to specify the magnitude and the direction
for displacement and velocity. These are VECTOR
quantities
Acceleration
Acceleration is the rate of change of velocity
a = ( v f - vi ) / t
Example 2.5 . . . Uniformly accelerating car
When the traffic light turns green, the speed
of a car increases uniformly from vi = 0 m/s
at t = 0 s to vf = 18 m/s at t =6 s
(a) Calculate the acceleration
(b) Calculate the speed at t = 4 s
(c) Calculate the distance traveled in 6 s
Solution 2.5 . . . Uniformly accelerating car
a = (Vf - Vi ) / t
a = (18 - 0) / 6
a = 3 m/s2
Vf = Vi + a t
Vf = 0 + 3x4
Vf at 4s = 12 m/s
Vave = (Vf + Vi ) / 2
Vave = d / t
Vave = (18+0)/2
9 m/s = d / 6 s
Vave = 9 m /s
d = 54 m
Example 2.6 . . . Motion in one dimension
• Is the speed constant at
t=10s?
• When is the acceleration
zero?
• When is it slowing down
(decelerating)?
• What is the acceleration
at t=7s?
Solution 2.6 . . . Motion in one dimension
• Is the speed constant at
t=10s? No
• When is the acceleration
zero? 13 s < t < 42 s
• When is it slowing down
(decelerating)? t > 42 s
• What is the acceleration
at t=7s? 1 m / s2
Equation Summary for uniform acceleration
(No Jerks Pleeeease!)
Vave = d / t
Vf = Vi + a t
Vave = (Vf + Vi) / 2
d = Vi t + 1/2 a t2
Vf2 = Vi2 + 2ad
Example 2.7 . . . Driver’s not a jerk!
A car accelerates from a stop light and attains
a speed of 24 m/s after traveling a distance of
72 m. What is the acceleration of the car?
Solution 2.7 . . . Driver’s not a jerk!
Given: Vi = 0
Solve for: a
Vf = 24 m/s
Formula Vf2 = Vi2 + 2ad
(24)2 = 0 + (2)(a)(72)
a = 4 m/s2
d = 72 m
Example 2.8 . . . Free Fall
Acceleration due to Earth’s gravity is 9.8 m/s2
(a) A cat falls off a ledge. How fast is it
moving 3 seconds after the fall?
(b) What is the distance traveled by the
unfortunate cat?
Solution 2.8 . . . Free Fall
Given: Vi = 0
Solve for: Vf
a = 9.8 m/s2
d
Formula Vf = Vi + a t
Vf = 0 + (9.8)(3)
Vf = 30 m/s
t=3s
d = Vi t + 1/2 a t2
d = 0 + (1/2)(9.8)(3)(3)
d = 44 m
Example 2.9 . . . Granny’s Orchard
Big apple is twice as big as Little apple. Both fall
from the same height at the same time. Which
statement is correct?
A. Both reach the ground at about the same time
B. Big reaches the ground way before Little does
C. Little reaches the ground way before Big does
Solution 2.9 . . . Granny’s Orchard
Big apple is twice as big as Little apple. Both fall
from the same height at the same time. Which
statement is correct?
A. Both reach the ground at about the same time
B. Big reaches the ground way before Little does
C. Little reaches the ground way before Big does
That’s all folks!