PHYS 201

Chapter 2: Kinematics in 1-D

DistanceDisplacementSpeedVelocityAccelerationEquations of Kinematics Free Fall

Distance (scalar, units: mi, ft, m, km, …)

How far an object travels.

Displacement (vector, units: mi, ft, m, km, …)The change in position.

(Shortest distance between two points. The vector points from initial to final point).

Average Speed (scalar, unit: mi/h (mph), ft/s, m/s, km/h, …)

The rate of distance change.

Velocity (vector, unit: mi/h (mph), ft/s, m/s, km/h, …)

The rate of displacement change.

Acceleration (vector, unit: mi/h2, ft/s2, m/s2, km/h2, …)

The rate of velocity change.

A car is moving with a constant speed of 20 mi/h at the Richland avenue round about in circle. When the car reaches to its initial point, its displacement is

(1) 2r

(2) 0

(3) 2r2

Initial and final points are the same. So displacement = 0.

CLICKER!

(radius: r = 50 ft, circumference = 2r)

A car is moving with a constant speed of 20 mi/h at the Richland avenue round about in circle. Which of the following is true?

(1) Velocity is constant.

(2) Velocity is zero.

(3) Velocity is changing.

Although the magnitude does not change, the direction changes. So the velocity is varying

CLICKER!

(radius: r = 50 ft, circumference = 2r)

A car is moving with a constant speed of 20 mi/h at the Richland avenue round about in circle. Which of the following is true?

(1) There is an acceleration.

(2) Acceleration is zero.

(3) Acceleration is constant.

Velocity changes, so there is an acceleration.

CLICKER!

(radius: r = 50 ft, circumference = 2r)

Ex. 1The distance between Athens and Columbus is 80 miles and it takes about 1 hr and 30 min to drive (of course, if you are not speeding!). What is the average speed you are driving?

Ex. 2A car travels in a straight line with an average velocity of 60 mi/hr for 1 hr and 30 min, and then it travels an average of 45 mi/h for 30 min in a road construction area.

(a) What is the total displacement?

(b) What is the average speed for the total trip?

(c) Draw a distance vs. time graph for (b).

Ex. 3You bike towards East with 30 mi/h for 30 min, and then15 mi/h towards North for 10 min. Find

(1) the total distance covered

(2) the average speed

(3) the total displacement

(4) the average velocity

(5) draw a distance vs. time plot for this trip. 

 

Equations of Kinematics for Constant Acceleration

V = V0 + at

x = ½ (V0 + V) t

x = V0t + ½ at2

V2 = V02 + 2 ax

Conditions: must moves in a straight line. must be a constant acceleration.

Ex. 4 A car accelerates uniformly from rest to a speed of 25 m/s in 8.0s.

Find the distance the car travels in this time and the constant acceleration of the car.Define the +x direction to be in the direction of motion of the car.   (1) V = V0 + at

(2) x = ½ (V0 + V) t

(3) x = V0t + ½ at2

(4) V2 = V02 + 2 ax

Ex. 5 [Plane Landing]A jet plane lands with a velocity of +100m/s and with full brakes it accelerates at a rate of -5.0m/s2. From the instant it touches the runway, what is the minimum time needed before it can come to rest? Can this plane land on a small island airport where the runway is 0.80km long?    (1) V = V0 + at

(2) x = ½ (V0 + V) t

(3) x = V0t + ½ at2

(4) V2 = V02 + 2 ax

Free Fall

Objects fall near the Earth surface moves with a constant acceleration due to gravity (if the air resistance is neglected).

The acceleration due to gravity g = -9.81 m/s2. All constant acceleration equations above can be applied. Following symbols are changed: ‘a’ = ‘g’, and ‘x’ = ‘y’.

Ex. 6A ball is thrown up into the air at a speed of 25 m/s. How high does the ball travel?         (1) V = V0 + gt

(2) y = ½ (V0 + V) t

(3) y = V0t + ½ gt2

(4) V2 = V02 + 2 gy

This position versus time graph represents the position of a person as a function of time. At what point or points is the velocity constant (not changing)?

(1) A

(2) D

(3) C

(4) A and D

(5) B and E

(6) A, B, D and EA

B

DCE

posi

tion

timeSlope represents the velocity. Anywhere slope is not changing, velocity is not changing!

At what point is the person moving fastest? B – the greatest slope

CLICKER!

Which velocity plot corresponds to the position plot to the right?

x vs t graph: Constant positive slope, then zero slope (zero v)

CLICKER!

A ball is tossed into the air. Assume the +y direction to be upwards. Which plot best represents the VELOCITY versus time of this graph?

Velocity starts upward (+), then transitions to downward (-).

CLICKER!

A ball is tossed into the air. Think about the direction of the acceleration as the ball is traveling upward and as it is traveling downward.

1. acceleration is upward when ball traveling up; downward when traveling down

2. acceleration is downward when ball traveling up; downward when traveling down

3. acceleration is upward when ball traveling up; upward when traveling down

4. acceleration is downward when ball traveling up; upward when traveling down

The force due to gravity does not change directions.

CLICKER!

A ball is tossed into the air. Think about the velocity and acceleration at the point when the ball reaches maximum height.

1. the velocity is zero and the acceleration is zero

2. the velocity is non-zero and the acceleration is zero

3. the velocity is zero and the acceleration is non-zero

4. the velocity is non-zero and the acceleration is non-zero

Even though velocity is zero right at max height, the gravity doesn't 'turn off' for split second.

CLICKER!

Ex. 7 You drop a stone into a well. It takes 2.3s for the stone to reach the bottom. How deep is the well?

y = ?

v0 = 0m/s

v = ?

a = 9.8 m/s2 down

t = 2.3 sy = v0t + (1/2)g t2

y = 0*(2.3s) + (0.5)(-9.8m/s2)(2.3s)2

y = -25.9 m or 25.9m below release point

Ex. 8You throw a rock from a bridge at a speed of 35 m/s straight down. How fast is it traveling when it hits the water 60m below and how much time does it take to travel the 60m?

y = -60m

v0 = -35m/s

v = ?

g = -9.8 m/s2

t = ?

v2 = v02 + 2 g y

v2 = (-35)2 + 2(-9.8)(-60m)

v = 49 m/s

v = v0 + g t

-49m/s = -35m/s + (-9.8)*t

t= 1.43 s

A

BC

C = A + B 2 2

= tan

A

B-1

1 ft = 12 in 1 m = 3.281 ft1 in = 2.54 cm1 mi = 1.601 km1 mi = 5280 ft

Unit Conversion

g = -9.81 m/s2

Acceleration due to gravity

(1) V = V0 + at

(2) x = ½ (V0 + V) t

(3) x = V0t + ½ at2

(4) V2 = V02 + 2 ax

QUIZ 1 Equations