motion in one dimension by: heather britton. motion in one dimension kinematics - the study of how...
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Motion In One Dimension
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)
Motion In One Dimension
Δx = x - xo
Δ = change
x = final position
xo = initial position
the subscript o indicates a beginning measurement
Motion In One Dimension
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
Motion In One Dimension
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
Motion In One Dimension
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)
Motion In One Dimension
Example 2
How much time does it take a person running at 9 m/s to complete a 100 m dash
Motion In One Dimension
Example 3
What is the displacement of a person riding a bicycle at a velocity of 15 m/s for 20 s?
Motion In One Dimension
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
Motion In One Dimension
An acceleration occurs when velocity changes
There are 3 ways an object can accelerate
1. Increase velocity
2. Decrease velocity
3. Change direction
Motion In One Dimension
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)
Motion In One Dimension
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?
Motion In One Dimension
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
Motion In One Dimension
We will start with the following presumptions
t1 = 0 t2 = t
x1 = xo x2 = x
v1 = vo v2 = v
Motion In One Dimension
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?
Motion In One Dimension
Example 6
Using the data from example 5 what was the average velocity during the period of acceleration?
Motion In One Dimension
Example 7
Using the data from example 5 how far did the car travel during the period of acceleration?
Motion In One Dimension
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?
Motion In One Dimension
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?