Motion In One Dimension by: Heather Britton

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 Dimension Distance - 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 - x o Δ = change x = final position x o = 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 Dimension Scalar 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 Dimension Velocity - 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 1 What is the velocity of a snail if it crawls 2 m in 80 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/s 2 )

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 t 1 = 0 t 2 = t x 1 = x o x 2 = x v 1 = v o v 2 = v

Motion In One Dimension Using a = Δx / Δt We get v = v o + at

Motion In One Dimension How to calculate position with uniform acceleration x = x o + v o + (1/2)at 2

Motion In One Dimension What to do when time is not known v 2 = v o 2 + 2a(x - x o )

Motion In One Dimension Example 5 A car is going 30 m/s and accelerates at the rate of 2 m/s 2 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/s 2 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?

Motion In One Dimension 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/s 2