Quick QuizQuick QuizConsider the graph at the right. The object

whose motion is represented by this graph is ... (include all that are true):

a)moving in the positive direction.b)moving with a constant velocity.c) moving with a negative velocity.d)slowing down.e)changing directions.f) speeding up.g)moving with a positive acceleration.h)moving with a constant acceleration.

Quick QuizQuick QuizCalculate the speed of the object

during all 3 motion segments depicted in the graph.

recallrecallspeed how fast an object is

moving

average speed the average of all instantaneous speeds; found by the distance/time ratio

instantaneous speed the speed at any given instant in time

instantaneous speedinstantaneous speedfor uniform motion, the

instantaneous velocity at any point will be the same as the average velocity across all points

for non-uniform motion (acceleration) these values will not necessarily be equal

instantaneous speed on a instantaneous speed on a non-uniform motion graphnon-uniform motion graph

moving along the acceleration curve, the slope progressively increases (as speed increases)

to determine instantaneous velocity we must calculate the slope of the tangent of the line on the p-t graph

a tangent is a straight line that contacts a curve at a single point

AccelerationAccelerationCalculations and Graphs

accelerationaccelerationdescribes how quickly an object’s

velocity changes over time (rate of change in velocity)

a vector quantity (directional)average acceleration is given by

the equation:aav = Δv = vf – vi

Δt tf - ti

the standard unit for acceleration is m/s2

constant accelerationconstant accelerationwhen an object changes its

velocity by the same amount each second

note: this is non-uniform motion since the speed is changing

directiondirectiondepends on:

◦if the object is speeding up or slowing down◦if the object is moving in a + or – direction

Rule of Thumb: ◦if an object is slowing down, then its

acceleration is in the opposite direction of its motion

◦if an object is speeding up, then its acceleration is in the same direction as its motion

In Example A, the object is moving in the positive direction (i.e., has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration.

In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down. According to our RULE OF THUMB, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration.

important note on important note on directiondirectionin physics, + and – signs have a

physical meaning

they indicate direction

-2m/s2 represents acceleration in a negative direction, it does not mean the acceleration value is less than 0!

determining acceleration determining acceleration from graphsfrom graphs

Time Velocity(s) (m/s)1 102 103 104 105 10

determining acceleration determining acceleration from graphsfrom graphs

Time Velocity(s) (m/s)1 102 203 304 405 50