Transcript Linear Kinematics : Velocity & Acceleration

Linear Kinematics : Velocity &
Acceleration
Speed
Displacement - the change in position in a particular
direction and is always a straight line segment from
one point to another.
Displacements are vector quantities and can be
combined in vector fashion.
Motion – the displacement of an object in relation to
objects that are considered to be stationary.
The rate of motion is called speed
e.g. you are riding a bike at 6 m/s
You travel 6 m in 1 second, 12 m in 2 seconds.
Speed can be graphed with
a displacement vs. time
graph.
Slope A = 3/1 = 3 m/s
Slope B = 3/3 = 1 m/s
Slope C =1/3 = 0.33 m/s
This graph shows three lines of constant speed. In
other words, the speed remained the same over the
entire displacement and the result is a straight line
graph.
The average speed is
found by dividing
the total distance by
the elapsed time. In
most cases objects
do not move with a
constant speed.
Initially and at the
end, the speed is
likely to be less.
Suppose you ride
your bike 120m in
20s. Your average
speed is = 6m/s
A graph of your speed might
look like fig 3-3
You start at 0.0 m/s, increase
to a constant speed between 3
and 15 s then begin to slow
down.
Instantaneous speed is the slope of the line at a point in
the line.
This would be shown by the slope of the line that is
tangent to the speed curve.
Without calculus, the only way to measure instantaneous
speed is to calculate the slope of a tiny portion of the
speed curve.
On our graph, the initial speed A is
approx. 3.9 m/s, the constant
speed B is approx. 7.5 m/s, and the
final speed C is approx. 4.5 m/s.
Speed is a scalar
quantity,
meaning that no
direction is
implied.
It is
t ot al distance
t ime
Velocity
Velocity is speed in a particular direction.
When you are given the speed of the object and the
direction it is headed, you know the velocity. This
makes it a vector quantity.
Remember velocity may be positive (+ve) or negative
(-ve) to indicate some direction.
average velocity =
v
v
total displaceme nt
total elapsed time
d f  di
t f  ti
d
t
Recall that ∆ is the Greek
symbol delta and means “change
in”
In this graph, (fig 34) the velocity over
the entire range is
constant
v
d 5
  0.5 m/s
t 10
Similarly, the velocity
between points A and B
on the graph is
v
d 1
  0.5 m/s
t 2
The motion of this object is said to be
uniform (i.e. it doesn't change through
the graph).
A graph with variable
motion is shown in
fig 3-5.
The average velocity is
v
d 5
  0.5 m/s
t 10
The velocity
between points C
& D is
v
d 2
 1 m/s
t 2
The velocity at the specific point
C is found by drawing the
tangent and finding its slope.
d 3 1 2
v

 1 m/s
t 6  2 2
The velocity at a specific instant
in variable motion is also called
instantaneous velocity.