Motion in One Dimension

Kinematics

Distance vs. Displacement

• Distance – how far you’ve traveled

Scalar quantity - 20 m

• Displacement – shortest distance traveled from starting point to end point.

Vector quantity – 20 m, 40o, N of W

Instantaneous Position

Where an object is located at one and only one time.

• At 1.0 s, object is at 3.0 m• At 2.0 s, object is at 6.0 m

Time (s) Position (m)

1.0 3.0

2.0 6.0

Remember the example? Change the paces to meters (m).

• Walk due west for 52 m, then walk 30.0Walk due west for 52 m, then walk 30.0oo North of North of West for 42 m, and then walk due north for 25 m. West for 42 m, and then walk due north for 25 m.

• The total distance traveled wasThe total distance traveled was

(52 + 42 + 25)m = 119 m

The total displacement is 99 Paces, 2899 Paces, 28oo, N of W, N of W

Speed

Speed is how fast an object is moving.

Scalar quantity = 30 km/h

Velocity

Velocity is how fast an object is moving in a certain direction.

Vector quantity =

30 km/h, 45o, S of E

Direction of Velocity (+)

Velocity is positive (+) if moving due east or due north.

N

E

Direction of Velocity (-)

• Velocity is negative (-) is moving due west or due south.

W

S

Constant Velocity

• Average velocity is the same for all time intervals.

Time

(s)

Velocity

(m/s)

1.0 30.

2.0 30.

Instantaneous Velocity

Speed and direction at one and only one time.

At 1.0 s, the instantaneous velocity is 35 m/s.

At 2.0 s, the instantaneous velocity is 55 m/s.

Time

(s)

Velocity

(m/s)

1.0 35

2.0 55

Average Velocity I

Change in displacement over a given time interval.

Equation: V = ∆d = d2 – d1

∆t t2 - t1

Unit of measurements: m/s, cm/s, ft/s, km/h,

and mi/h

Average Speed

Total distance traveled over total time

Equation: V = dt = d1 + d2 +..

tt t1 + t2 + …..

Units of Measurements: m/s, cm/s, ft/s, km/h,

and mi/h

Conversions

• Kilo = 1000 1 Km = 1000 m

• 1 mi. = 1609 km

• 1 h = 3600 s

• Change 20.0 m/s to Km/h

20.0 m x 1 Km x 3600 s = 72 km/h s 1000 m 1 h

Example 1

• A person walks 13 km in 2.0 h. What is the person’s average velocity in km/h and m/s?

V = ∆d = d2 – d1 = 13 km = 6.5 km/h

∆t t2 - t1 2.0 h

6.5 Km x 1000 m x 1h = 1.8 m/s

h 1 Km 3600 s

Example 2

A car traveled 2.0 mi. in 0.2 h, 5.0 mi in 0.6 h

and 15.0 mi in 1.0 h. What was the average speed of the car?

V = dt = d1 + d2 + d 3

tt t1 + t2 + t3

= 2.0 mi + 5.0 mi + 15.0 mi = 12 mi/h = 10 mi/h

0.2 h + 0.6 h + 1.0 h

Example 3

A car traveled 2.0 h at a speed of 50 mi/h and 4.0 h at 75 mi/h. Calculate the average speed.

V = (2.0 h x 50. mi/h) + (4.0 h x 75 mi/h) 2.0 h + 4.0 h

V = 67 mi/h

Example 4

• A toy train starts at 0 m and runs around the 1.0 m track in 30 s. train stops at the starting point.

What was its average speed?

V = 1.0 m/30 s = 0.03 m/s

What was its average velocity?

V = 0 m/s. It stopped at its starting point.

The change in displacement is 0.

Average Acceleration

• Change in velocity over a period of time.

a = ∆V = V2 – V1

∆t t2 - t1

Units of measurements: m/s2, cm/s2, ft/s2

km/h2, and mi/h2

Direction of Acceleration

• Positive if the change in velocity is positive.

∆V = 40 m/s – 20 m/s = + 20 m/s

Acceleration is increasing.

• Negative if the change in velocity is negative.

∆V = 20 m/s – 40 m/s = -20 m/s

Acceleration is decreasing. (decelerating)

Acceleration Example

An Indy-500 race car’s velocity increases from +4.0 m/s to +36 m/s over a 4.0 s period. What is its average acceleration?

V 1 = +4.0 m/s

V2 = +36.0 m/s

∆t = 4.0 s

a = ∆V = +36.0 m/s – +4.0 m/s = 8.0 m/s2

∆t 4.0 s