Motion

• Motion: when an object changes its position.
• Dependent on the reference point.
• Reference point: an indicator that orients you; the place from where you measure, record, or witness an event.
• Ex. Consider the reference point when describing the motion of a car.

Measuring Motion

• Distance: (d) how far an object has moved.
• Can be measured in m, in, ft, mi, etc.
• Displacement: (Δx) distance and direction of an object’s change in position; difference from starting to ending point.
• Ex. If a runner runs around a 400 m track and ends where they started, they have traveled a distance of 400 m, but have been displaced 0 m.

Example #1

d = 50 + 20

d = 70 m

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Δx = 50 – 20

Δx = 30 m North

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If a soccer player runs after his opponent 50 m North, then turns around and chases him 20 m South, what is his distance and displacement? Use the picture to the right to help you.

d = ?

Δx = ?

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50 m

20 m

Measuring Motion

• If an object travels at a right angle, the Pythagorean theorem is used to find the displacement.

a² + b² = c²

Δx

Sometimes finding displacement isn’t as easy.

a

b

c

• c (the hypotenuse of the right triangle) would be the displacement (Δx)
• Note: This will not need to be used every time you find displacement!!

Example #2

a² + b² = c²

Δx

a

b

c

A delivery truck drives 4 miles West before turning right and driving 6 miles North to make a delivery. Find the delivery truck’s distance and displacement.

a = 4 miles

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b = 6 miles

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c = Δx = ?

4 miles

6 miles

d = 4 + 6

d = 10 mi

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a² + b² = c²

4² + 6² = c²

16 + 36 = c²

52 = c²

7.21 = c

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√

√

c = 7.21

Δx = 7.21 mi Northwest

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Measuring Motion

• Speed: (s) the distance an object travels per unit of time.
• Can be measured in m/s, mi/hr, ft/min, km/hr, etc.

s =

d

t

Calculating Speed

s = 2 km

10 min

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s = 0.2 km/min

s = ?

d = 2 km

t = 10 min

s = d

t

Example #3: Suppose you ran 2 km in 10 min. With what speed did you run?

Calculating Speed

t = ?

s = 343 m/s

d = 2 km

1 km

1000 m

=

2000 m

s = d

t

(t)

(t)

t s = d

s

s

t = d

s

t = 2000 m

343 m/s

t = 5.83 s

Example #4: Sound travels at 343 m/s through dry air. If a lightning bolt strikes the ground 2 km away from you, how long will it take for the sound to reach you?

Two Types of Speeds

• Average speed: total distance traveled divided by total time traveled.
• Ex. If I’m driving to Clemson to watch the National Championship football team play, it is a total distance of 300 miles from my house. If it takes me 5 hours to get there, my average speed is 60 mi/hr.

• Instantaneous speed: the speed at any given point – what shows up on your speedometer.
• Ex. On my trip to Clemson, at some points on the highway my instantaneous speed is 70 mi/hr. At stoplights, my instantaneous speed is 0 mi/hr.

Velocity

• Velocity: (v) the speed of an object and the direction of its motion.
• Speed can remain constant and velocity change if the object is changing direction.
• Calculated the same as speed, just must include direction in your answer!!

v =

d

t

Practice Time

1. A girl is training to run a 5k (3.1 mile) race. If she runs a trial race in 0.5 hours, what is her average speed?

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• An elevator at a museum can travel 210 m upwards in 35 s. What is the elevator’s velocity?

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• How far does a car travel in .75 hrs if it is moving at a constant speed of 45 mi/hr?

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• If a motorcycle is moving at a constant speed down the highway of 40 km/hr, how long would it take the motorcycle to travel 10 km?

Answer: s = 6.2 mi/hr or 10 km/hr

Answer: v = 6 m/s upwards

Answer: d = 33.75 mi

Answer: t = 0.25 hr

Graphing Motion

• Slope: the steepness of a line.
• Calculated as rise = Δy

• On a distance vs. time graph, this means…

Graphs can visually help us to understand an object’s motion.

run Δx

• Calculated as rise = Δy = distance

run Δx time

• Therefore on a distance vs. time graph, the slope = speed.

Graphing Motion

Describe the motion of each graph.

The object is moving at a constant speed, away from the reference point.

The object is moving at a constant speed, coming towards the reference point.

The object is speeding up, due to the line becoming steeper.

The object is slowing down, due to the line leveling out.

Graphing Motion

Sketch a graph that would show an object not moving.

Sketch a graph that would show an object moving at a constant speed, stopping, then speeding up.