Physics 101 lecture 4 and 5 note, Lecture notes of Software Engineering

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Physics 111: Mechanics

Lectures 4 and 5

Sharafadeen Adeniji

NUN Physics Department

Motion along a straight line

Motion

Position and displacement

Average velocity and average speed

Instantaneous velocity and speed

 Acceleration

Constant acceleration: A special

case

Free fall acceleration

4 Basic Quantities in

Kinematics

One Dimensional Position x

 (^) Motion can be defined as the change of position over time.  (^) How can we represent position along a straight line?  (^) Position definition:  (^) Defines a starting point: origin (x = 0), x relative to origin  (^) Direction: positive (right or up), negative (left or down)  (^) It depends on time: t = 0 (start clock), x(t=0) does not have to be zero.  (^) Position has units of [Length]: meters. x = + 2.5 m x = - 3 m

Quantities in Motion

Any motion involves three concepts

 (^) Displacement  (^) Velocity  Acceleration

These concepts can be used to study

objects in motion.

Displacement

 (^) Displacement is a change of position in time.  (^) Displacement:  (^) f stands for final and i stands for initial.  (^) It is a vector quantity.  (^) It has both magnitude and direction: + or - sign  (^) It has units of [length]: meters.  x  xf ( tf ) xi ( ti ) x 1 (t 1 ) = + 2.5 m x 2 (t 2 ) = - 2.0 m Δx = -2.0 m - 2.5 m = -4.5 m x 1 (t 1 ) = - 3.0 m x 2 (t 2 ) = + 1.0 m Δx = +1.0 m + 3.0 m = +4.0 m

Velocity

 (^) Velocity is the rate of change of position.  (^) Velocity is a vector quantity.  (^) Velocity has both magnitude and direction.  (^) Velocity has a unit of [length/time]: meter/second.  (^) We will be concerned with three quantities, defined as:  (^) Average velocity  (^) Average speed  (^) Instantaneous velocity avg total distance s t   0 lim t x dx v   t dt     t x x t x v f i avg       displacement distance displacement

Average Velocity

 (^) Average velocity is the slope of the line segment between end points on a graph.  (^) Dimensions: length/time (L/T) [m/s].  (^) SI unit: m/s.  (^) It is a vector (i.e. is signed), and displacement direction sets its sign.

t

x x

t

x

v

f i avg

Instantaneous Velocity

 (^) Instantaneous means “at some given instant”. The instantaneous velocity indicates what is happening at every point of time.  (^) Limiting process:  (^) Chords approach the tangent as Δt => 0  (^) Slope measure rate of change of position  (^) Instantaneous velocity:  (^) It is a vector quantity.  (^) Dimension: length/time (L/T), [m/s].  (^) It is the slope of the tangent line to x(t).  (^) Instantaneous velocity v(t) is a function of time. 0 lim t x dx v   t dt

 (^) Uniform velocity is the special case of constant velocity  (^) In this case, instantaneous velocities are always the same, all the instantaneous velocities will also equal the average velocity  (^) Begin with then

Uniform Velocity

t x x t x v f i x 

x f  xi  vx  t

x x(t) 0 t xi xf v v(t) 0 t tf vx ti Note: we are plotting velocity vs. time