Motion in One Dimension

x dx t dt Motion in One Dimension

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

Displacement  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 The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Dx = x - xo = 6 m - 2 m = 4 m Note:Displacement to the right is positive

Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Dx = x - xo = -6 m - 6 m = -12 m Note:Displacement to the left is negative

Displacement The displacement of a particle is defined as its change in position. x (m) -6 -4 -2 0 2 4 6 Dx = x - xo = (2 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

Displacement 70 m West 30 m East 40 m East 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

Velocity x2 Dx x1 Dt t1 t2 Average velocity The average velocity of a particle is defined as x Velocity is represented by the slope on a displacement-time graph t

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

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

Sample Problems: http://dev.physicslab.org/Document.aspx?doctype=5&filename=Kinematics_AverageSpeedAverageVelocity.xml Graphing Notes before Next Page

Motion Diagrams

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.

Acceleration v2 Dv v1 Dt t1 t2 Average acceleration The average acceleration of a particle is defined as the change in velocity Dvx divided by the time interval Dt during which that change occurred. v Acceleration is represented by the slope on a velocity-time graph t

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/s2. 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.

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

Sample Problem (HP book)

Motion in One Dimension