Motion in One Dimension dx dt x t

2-01 Displacement 2-02 Velocity 2-03 Acceleration 2-04 Motion Diagrams Motion in One Dimension Sections 2-05 One Dimensional Motion with Constant Acceleration 2-06 Freely Falling Objects

v  In the study of kinematics, we consider a moving object as a particle. A particle is a point-like mass having infinitesimal size and a finite mass. Kinematics is a part of dynamics In kinematics, you are interested in the description of motion Not concerned with the cause of the motion Displacement

0246 22 44 66 x The displacement of a particle is defined as its change in position. (m)  x = x  x o = 6 m  2 m = 4 m Note: Displacement to the right is positive

0246 22 44 66 x The displacement of a particle is defined as its change in position. (m)  x = x  x o =  6 m  6 m =  12 m Note: Displacement to the left is negative Displacement

0246 22 44 66 x The displacement of a particle is defined as its change in position. (m)  x = x  x o = (  m)  (  6 m) = 8 m Note: Displacement to the right is positive Displacement

Defined as the change in position – f stands for final and i stands for initial –May be represented as  y if vertical –Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary

EastWest 70 m 30 m Displacement East 40 m Displacement A student walks 70 m East, then walks 30 km West. What is the magnitude of the students net displacement? A) 30 m B) 40 m C) 70 m D) 100 m

Average velocity The average velocity of a particle is defined as x t x1x1 x2x2 t1t1 t2t2 xx tt Velocity is represented by the slope on a displacement-time graph Velocity

Average speed The average speed of a particle is defined as Velocity

Instantaneous velocity The instantaneous velocity v, equals the limiting value of the ratio xx tt x t Instantaneous velocity is represented by the slope of a displacement-time graph Velocity Instantaneous speed The instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity.

me=Kinematics_AverageSpeedAverageVelocity.xml Sample Problems: Graphing Notes before Next Page

Motion Diagrams

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s. Motion Diagrams

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s. Motion Diagrams (con’t)

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s. Motion Diagrams (con’t)

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s. Motion Diagrams (con’t)

The displacement versus time for a certain particle moving along the x axis is shown below. Find the average velocity in the time intervals (a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d) 4 s to 7 s (e) 0 to 8 s. Motion Diagrams (con’t)

Average acceleration The average acceleration of a particle is defined as the change in velocity  v x divided by the time interval  t during which that change occurred. v t v1v1 v2v2 t1t1 t2t2 vv tt Acceleration is represented by the slope on a velocity-time graph Acceleration

A new car manufacturer advertises that their car can go "from zero to sixty in 8 s". This is a description of A) instantaneous acceleration. B) average speed. C) instantaneous speed. D) average acceleration.

Acceleration A moving car experiences a constant acceleration of 1.5 m/s 2. This means the car is A) traveling at 1.5 m/s in every second. B) changing its velocity by 1.5 m/s. C) increasing its velocity by 1.5 m/s in every second. D) increases its displacement by 1.50 m each second.

True or False? (a) A car must always have an acceleration in the same direction as its velocity Quick Quiz 2.2 (b) It’s possible for a slowing car to have a positive acceleration (c) An object with constant nonzero acceleration can never stop and stay stopped. False True

Sample Problem (HP book)