motion in one dimension by: heather britton. motion in one dimension kinematics - the study of how...

Motion In One Dimension

by: Heather Britton


Kinematics - the study of how objects move

Frame of reference - what you are comparing the motion to

Represented by coordinate axes

For one dimension we will use the x axis

Motion In One DimensionDistance - how far an object moves (dependent on the path taken)

Displacement - the change in position of an object

Represented by x, y, or z

Measured in meters (the SI unit for distance)


Δx = x - xo

Δ = change

x = final position

xo = initial position

the subscript o indicates a beginning measurement


Magnitude - a numerical value describing the size of a quantity

For example:

If a person starts from zero and walks five meters to the right the magnitude of the displacement is five meters

Motion In One DimensionScalar quantity - a measurement that contains magnitude only

Examples include mass, volume, time and speed

Vector quantity - a measurement that contains both magnitude and direction

Examples include velocity, acceleration, and force


Vector quantities are represented in diagrams by an arrow

The length of the shaft represents the magnitude of the vector

The direction of the arrow shows the direction of the vector


Speed - the change in distance divided by the change in time

speed = Δdistance / Δtime

Motion In One DimensionVelocity - the change in displacement divided by the change in time

v = Δx / Δt

v = velocity measured in meters per second (m/s)

Δx = change in displacement (m)

Δt = change in time (s)


Example 1

What is the velocity of a snail if it crawls 2 m in 80 s?


Example 2

How much time does it take a person running at 9 m/s to complete a 100 m dash


Example 3

What is the displacement of a person riding a bicycle at a velocity of 15 m/s for 20 s?


These examples are valid when the velocity is constant

We can also use this equation to find the average velocity

Instantaneous velocity - the change in displacement over a very small time interval


An acceleration occurs when velocity changes

There are 3 ways an object can accelerate

1. Increase velocity

2. Decrease velocity

3. Change direction


Acceleration - the change in velocity divided by the change in time

a = Δv / Δt

a = acceleration measured in meters per second per second (m/s2)


Example 4

The velocity of a car increases from 2 m/s at 1 s to 16 m/s at 4.5 s. What is the car’s average acceleration?


For this class we will assume that all accelerations are constant

Therefore average acceleration and instantaneous acceleration are the same

Using the velocity and acceleration equations we will derive the constant acceleration equations


We will start with the following presumptions

t1 = 0 t2 = t

x1 = xo x2 = x

v1 = vo v2 = v


Using

a = Δx / Δt

We get

v = vo + at


How to calculate position with uniform acceleration

x = xo + vo + (1/2)at2


What to do when time is not known

v2 = vo2 + 2a(x - xo)


Example 5

A car is going 30 m/s and accelerates at the rate of 2 m/s2 for 4 s. What is its final velocity?


Example 6

Using the data from example 5 what was the average velocity during the period of acceleration?


Example 7

Using the data from example 5 how far did the car travel during the period of acceleration?


Example 8

A car moving at 2 m/s accelerates uniformly at 4.1 m/s2 for 7 s. How far does the car move?


Example 9

To take off an airplane must have a velocity of 71 m/s. If the runway is 1 km long, what is the minimum acceleration needed by the plane to safely take off?


Unsupported objects fall toward Earth due to the force of gravity

Gravity causes an acceleration

The acceleration of gravity on Earth in the absence of air resistance is a constant value

g = 9.8 m/s2

motion in one dimension by: heather britton. motion in one dimension kinematics - the study of how...

Documents

velocity changesthere

dimensionan acceleration

instantaneous acceleration

cars average acceleration

displacement mt

time smotion

x axismotion

motion torepresented