motion in one-direction: displacement, velocity, & acceleration

MOTION IN ONE-DIRECTION:DISPLACEMENT, VELOCITY, &

ACCELERATION

PHYSICS

Question• Is the book on your instructor’s desk in motion?

Explain your answer.

Frame of Reference

• A system for specifying the precise location of objects in space and time.

Introduction

• Kinematics is the science of describing the motion of objects using words, diagrams, graphs, and equations.

• In physics, we use these words as the language of kinematics. 1. Distance and Displacement 2. Speed and Velocity3. Acceleration

• These quantities is either a vector or scalar.

1. Scalars are quantities which are described by a magnitude only.

2. Vectors are quantities which are described by both a magnitude and a direction.

Distance Displacement

Distance refers to the total length of travel irrespective of the direction of the motion.

It is a scalar quantity.SI unit: meter (m) Other common units: kilometer (km), centimeter (cm)

Displacement refers to the distance moved in a particular direction. It is the object's overall change in position.

It is a vector quantity. SI unit: meter (m)Other common units: kilometer (km), centimeter (cm)

Displacement• When things start moving, the length of a

straight line drawn from the object’s initial position to it’s final position is it’s displacement

• In one dimension…

if xxx

Change in position along x-axis = (final position on x-axis) – (initial position on x-axis)

Motion in One Dimension

• Same concepts apply to any axis!Space shuttles instead of trains

if yyy

Change in position along y-axis = (final position on y-axis) – (initial position on y-axis)

Example 1• Is the displacement positive or negative?

Example 2• Is the displacement positive or negative?

Example 3

1. A student walks 4 meters East and 2 meters South.

2. A student walks 4 meters East, 2 meters South, 4 meters West, and 2 meters North.

Speed VelocitySpeed is the rate of change of distance.

It is a scalar quantity.

Velocity is the distance travelled in a specific direction. It is also defined as the rate of change of displacement.

It is a vector quantity.

Problems 1-6

IdentifyPlanSolve

Conversions

Instantaneous Speed and Average Speed As an object moves, it often undergoes changes in speed. The speed at any instant is known as the instantaneous speed. (From the value of the speedometer)

The average speed of the entire journey can be calculated:

tx

taken timeTotal

d travelledistance TotalSpeed Average

The direction of the object keeps changing.

Speed Vs VelocityAn object is moving in a circle at a constant speed of 10 m/s. We say that it has a constant speed but its velocity is not constant. Why?

Direction of Motion

How to Make a Graph

Time (sec) Position (meter)0 0

1 2

2 4

3 6

4 8

5 10

6 12

Interpreting Velocity Graphically

Object 1: positive slope = positive velocityObject 2: zero slope= zero velocity Object 3: negative slope = negative velocity

For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph.If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.

Slope

Instantaneous Velocity

The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.

Quiz Time