Download Motion in a Line

Physics-Motion in a line
Dr. J Seale
Objectives
Describe motion in a straight line.
 Define the equations of motion in terms of
displacement, velocity, and acceleration.
 Demonstrate the ability to solve problems
in physics relation to the motion of an
object.

What is Motion
Mechanics: study of the motion of an
objects, and the related concepts of force
and energy.
 Kinematics: motion of objects.
 Dynamics: deals with force and why
objects move.

Translational motion

We will begin with the motion of an
object in a straight line without
rotation.
 motion is along the same line.
 all parts of the object move
together at the same velocity.
Distance/Displacement
Distance refers to how far an object has
traveled. (Scaler)
 Displacement refers to the change in
position of an object (Vector).

Final position X2
 Initial Position X1
 Displacement ΔX = (X2 - X1)

Speed/Velocity

Speed refers to how far an object travels in a
given amount of time.


(distance/time)
Average velocity refers to the change in position
over a change in time.




Average Velocity = displacement/elapsed time
Vave = ΔX/ Δt
Instantaneous velocity is average velocity during a
instant.
v = lim (Δt -> 0) ΔX/Δt
acceleration

Acceleration refers to the change in
velocity with respect to time.
Positive acceleration is in the same direction
as the motion.
 a = Δv / Δt
 Units are m/s2

Distance, velocity and Acceleration

We now know that:
Displacement Δx = (x2 - x1)
 v = Δx/ Δt = (x2 - x1) / Δt
 a = Δv / Δt = (v2 - v1) / Δt


Also:

Δx = ½ at2
Equations of Motion

Using the appropriate math (algebra and
calculus) and assuming x0 and v0 are are
initial position and velocity:

x = x0 + vt

x = x0 + v0t + ½ at2

v = v0 + at

v2 = v02 + 2a(x - x0)