1. Lecture 5: Introduction to Physics PHY101
Chapter 2:
Distance and Displacement, Speed and Velocity (2.1,2.2)
Acceleration (2.3)
Equations of Kinematics for Constant
Acceleration (2.4) 1

2. Displacement and Distance
Displacement is the vector that points from a body’s initial position, x0, to its final position, x. The length of the displacement vector is equal to the shortest distance between the two positions.
x = x –x0
Note:
The length of x is (in general) not the same as distance
traveled !

3. Average Speed and Velocity
Average speed is a measure of how fast an object moves on average:
average speed = distance/elapsed time
Average speed does not take into account the direction of
motion from the initial and final position.

4. Average Speed and Velocity
Average velocity describes how the displacement of an object changes over time:
average velocity = displacement/elapsed time
vav = (x-x0) / (t-t0) = x / t
Average velocity also takes into account the direction of
motion.
Note:
The magnitude of vav is (in general) not the same as the
average speed !

5. Instantaneous Velocity and Speed
Average velocity and speed do not convey any information about how fast the object moves at a specific point in time.
The velocity at an instant can be obtained from
the average velocity by considering smaller and smaller time intervals, i.e.
Instantaneous velocity:
v = lim  t-> 0 x / t
Instantaneous speed is the magnitude of v.

6. Concept Question
If the average velocity of a car during a trip along a straight road is positive, is it possible for the instantaneous velocity at some time during the trip to be negative?
1 - Yes
2 - No
correct
If the driver has to put the car in reverse and back up some time
during the trip, then the car has a negative velocity. However,
since the car travels a distance from home in a certain amount of
time, the average velocity will be positive.

7. Acceleration Average acceleration describes how the velocity
of an object moving from the initial position to
the final position changes on average over time:
aav = (v-v0) / (t-t0) = v / t
The acceleration at an instant can be obtained from
the average acceleration by considering smaller and smaller time intervals, i.e.
Instantaneous acceleration:
a = lim  t-> 0 v / t

8. Concept Question
If the velocity of some object is not zero, can its acceleration ever be zero ?
1 - Yes
2 - No
correct
If the object is moving at a constant velocity,
then the acceleration is zero.

9. Concept Question
Is it possible for an object to have a positive velocity at the same time as it has a negative acceleration?
1 - Yes
2 – No
correct
An object, like a car, can be moving forward
giving it a positive velocity,
but then brake, causing deccelaration which is
negative.

10. Kinematics in One Dimension Constant Acceleration
Simplifications:
In one dimension all vectors in the previous equations
can be replaced by their scalar component along one axis.
For motion with constant acceleration, average and
instantaneous acceleration are equal.
For motion with constant acceleration, the rate with which
velocity changes is constant, i.e. does not change over time.
The average velocity is then simply given as
vav = (v0 +v)/2

11. Kinematics in One Dimension Constant Acceleration
Consider an object which moves from the initial position x0, at time t0
with velocity v0, with constant acceleration along a straight line.
How does displacement and velocity of this object change with time ?
a = (v-v0) / (t-t0) => v(t) = v0 + a (t-t0) (1)
vav = (x-x0) / (t-t0) = (v+v0)/2 => x(t) = x0 + (t-t0) (v+v0)/2 (2)
Use Eq. (1) to replace v in Eq.(2):
x(t) = x0 + (t-t0) v0 + a/2 (t-t0) (3)
Use Eq. (1) to replace (t-t0) in Eq.(2):
v2 = v a (x-x0 ) (4)

12. Summary of Concepts kinematics: A description of motion
position: your coordinates
displacement: x = change of position
velocity: rate of change of position
average : x/t
instantaneous: slope of x vs. t
acceleration: rate of change of velocity
average: v/t
instantaneous: slope of v vs. t