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). Displacement and Distance.
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x = x –x0
The length of xis (in general) not the same as distance
average speed = distance/elapsed time
Average speed does not take into account the direction of
motion from the initial and final position.
average velocity = displacement/elapsed time
vav = (x-x0) / (t-t0) = x/ t
Average velocity also takes into account the direction of
The magnitude of vav is (in general) not the same as the
average speed !
the average velocity by considering smaller and smaller time intervals, i.e.
v = lim t-> 0x/ t
Instantaneous speed is the magnitude of v.
1 - Yes
2 - No
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.
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 average acceleration by considering smaller and smaller time intervals, i.e.
a = lim t-> 0v/ t
1 - Yes
2 - No
If the object is moving at a constant velocity,
then the acceleration is zero.
1 - Yes
2 – No
An object, like a car, can be moving forward
giving it a positive velocity,
but then brake, causing deccelaration which is
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
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) 2 (3)
Use Eq. (1) to replace (t-t0) in Eq.(2):
v2 = v02 + 2 a (x-x0 ) (4)