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UNIT 1: 1-D KINEMATICS
Lesson 5:
Kinematic Equations
CENTRE HIGH: PHYSICS 20
Reading Segment:
Kinematic Equations
To prepare for this section, please read:
Unit 1: p.19
Kinematic Equations
When an object has a constant acceleration,
there are many equations which describe the motion.
A complete list of equations is on the next page
(and on your formula sheet)
Here is a list of all the equations:
a = vf - vi vf2 = vi
2 + 2 a d
t
d = vi t + 0.5 a t2 d = vf t - 0.5 a t2
d = vi + vf t
2
where vavg = vi + vf
2
To figure out which equation to use, you make a list of
the 5 kinematic variables:
vi, vf, a, d, t
If you can identify the variable that is NOT involved
in the question, you can choose the proper equation.
This will be illustrated in the next pages.
Variables involved in question:
vi, vf, a, t
Variable NOT involved in the question:
d
Equation to use: a = vf - vi
t
This is the only kinematic equation that
does not have displacement (d) in it.
Variables involved in question:
vi, vf, a, d
Variable NOT involved in the question:
t
Equation to use: vf2 = vi
2 + 2 a d
This is the only kinematic equation that
does not have time (t) in it.
The process is similar for the other equations:
Equations Variables
vi vf a d t
d = vi t + 0.5 a t2
d = vf t - 0.5 a t2
d = vi + vf t
2
Note:
If the object has a constant velocity:
- the acceleration is zero
- the final velocity is equal to the initial velocity (vi = vf)
Use the equation: v = d
t
Ex. 1 A ball is rolled up a constant incline at a speed of 9.0 m/s.
How much time is required to reach a maximum
displacement of 6.45 m ?
Diagram: Rest
9.0 m/s 6.45 m
If it has reached its maximum displacement,
then it cannot go any higher.
Thus, it has come to rest (vf = 0)
List: Ref: Up slope is positive
vi = +9.0 m/s Down is negative
vf = 0
a d = +6.45 m
t ?
Make a list of the kinematic variables.
Be certain you get the right sign for the vector quantities.
List: Ref: Up slope is positive
vi = +9.0 m/s Down is negative
vf = 0
a d = +6.45 m
t ?
d = vi + vf t
2
This is the only equation that does not
have acceleration (a) in it.
d = vi + vf t
2
d = vi + vf t
2
d = vi t
2
Since vf = 0, then remove this variable from the equation.
d = vi t
2
2 d = vi t
t = 2 d = 2 (6.45 m)
vi 9.0 m/s
= 1.4 s
Ex. 2 A particle experiences an acceleration of 470 m/s2 North
for a total time of 960 milliseconds. If its displacement
is 0.123 km South, then find the initial velocity.
List: Ref: North is positive
vi = ? South is negative
vf
a = +470 m/s2
d = -0.123 103 m = -123 m
t = 960 10-3 s = 0.960 s
Make a list of the kinematic variables.
Be certain you get the right sign for the vector quantities
and all quantities are in standard units.
List: Ref: North is positive
vi = ? South is negative
vf
a = +470 m/s2
d = -0.123 103 m = -123 m
t = 960 10-3 s = 0.960 s
Equation: d = vi t + 0.5 a t2
This is the only equation that does not have
the final velocity (vf) in it.
d = vi t + 0.5 a t2
d - 0.5 a t2 = vi t
vi = d - 0.5 a t2
t
= (-123 m) - 0.5 (470 m/s2) (0.960 s)2
0.960 s
= -354 m/s
vi = 354 m/s South
Practice Problems
Try these problems in the Physics 20 Workbook:
Unit 1 p. 10 #1 - 10