Notes: 11.2
Speed & Velocity
Speed
A. The ratio of the distance an object
moves to the amount of time the object
moves.
B. The SI unit of speed is m/s. However, it
is useful to use km/h when talking about
the speed of a car.
Average Speed
A. Average speed is computed for the
entire duration of a trip.
B. Average speed or “v” is the total
distance traveled, “d”, divided by the
time, “t”, it takes to travel that distance.
C. Average Speed = Total distance / Total
time or v = d/t.
Example 1
While traveling on vacation, you measure
the times and distances traveled. You
travel 35 km in 0.4 hour, followed by 53 km
in 0.6 hour. What is your average speed?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Example 2
A person jogs 4.0 kilometers in 32 minutes,
then 2.0 kilometers in 22 minutes, and
finally 1.0 kilometer in 16 minutes. What is
the jogger’s average speed in kilometers
per minute?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Example 3
A train travels 190 kilometers in 3.0 hours,
and then 120 kilometers in 2.0 hours. What
is its average speed?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Example 4
A car travels 85 km from Baltimore to
Columbus, then 45 km from Columbus to
Polaris. The total trip took 1.5 hours. What
was the average speed of the car?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Example 5
A bicyclist travels for 1.5 hours at an
average speed of 32 km/h. How far does
the bicyclist travel in that time?
What do we know?
What do we want to know?
What formula should we use?
Solve!
Instantaneous Speed
A. Instantaneous speed is measured at a
particular instant.
B. Instantaneous speed, “v”, is the rate at
which an object is moving at a given
moment in time.
Ex.) The speed of a car traveling on state
route 256 is 55 miles per hour.
Graphing Motion
A. Time is graphed on the x - axis while
distance is graphed on the y - axis.
B. Slope = rise / run
1. In a distance time graph the slope
is the change in the vertical axis
value divided by the change in the
horizontal axis value.
2. This is equal to average speed.
C. A steeper slope on a distance - line
graph indicates a higher speed while a
less steep slope indicates a slower speed.
Graphing Motion
D. Graphs A and B show constant speed
and graph C shows varying speed.
500
400
300
200
100
0
4
8 12 16 20
0
4
8
12 16 20
0
4
8
12 16 20
1. Graph A: Total Distance = ____________
Total Time
= ____________
Average Speed
= ____________
2. Graph B: Total Distance = ____________
Total Time
= ____________
Average Speed
= ____________
D1 = _______ T1 = ________ V1 = _________
D2 = _______ T2 = ________ V2 = _________
D3 = _______ T3 = ________ V3 = _________
D4 = _______ T4 = ________ V4 = _________
D5 = _______ T5 = ________ V5 = _________
Total Distance = _____________
Total Time
= _____________
Average Speed = _____________
Velocity
A. Velocity is the speed and direction in
which an object is moving.
B. Since velocity has speed and direction it
is a vector.
1. Smaller vectors represent slower
speeds and longer vectors represent
faster speeds.
2. Not only are vectors different sizes
but they also point in different
directions to represent the direction
of a moving object.
Velocity
3.Therefore a change in velocity can
be the result of a change in speed,
direction, or both.
4. An object moving in a straight line
has constant velocity or uniform
motion.
Combining Velocities
A. When an object is moving with more
than one velocity we can add the
velocities.
1. This is called vector addition.
Vector Addition
Ex.1) the velocity of the river relative to the
riverbank (x) and the velocity of the boat
relative to the river (y) combine. They yield
the velocity of the boat relative to the
riverbank (z).
Vector Addition
Ex.2) The relative velocities of the current (x) and
the boat (y) are at right angles to each other.
Adding these velocity vectors yields a
resultant velocity.