Kinematics Equations
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Specific Outcomes:
i. I can define, qualitatively and quantitatively, displacement, velocity
and acceleration.
ii. I can define, operationally, and compare and contrast scalar and
vector quantities.
iii. I can interpret, quantitatively, the motion of one object relative to
another, using displacement and velocity vectors.
Kinematics Equations
Kinematics Equations
There are five main equations in kinematics,
that apply to both horizontal and vertical
situations
The first equation is
used with average
speed or velocity:
d = vavet
Kinematics Equations
The rest involve initial and/or final velocity:
vf - vi
where:
a=
t
vi = initial velocity in m/s
where:
vave = average velocity
in m/s
d=
( )
vi + vf
2
t
vf = final velocity in m/s
d = displacement in m
d = displacement in m
d = vit + ½at2
t = time in s
t = time elapsed in s
vf2 = vi2 + 2ad
a = acceleration in m/s2
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
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Kinematics Equations
Kinematics Equations
Select equations based on variables:
Equation
v -v
a= ft i
v +v
d= i 2 f t
d or ∆d
d = vit + ½at2
x
x
vf2 = vi2 + 2ad
x
x
(
)
a
vf
vi
t or ∆t
x
x
x
x
x
x
x
x
x
x
x
Also useful is the equation that averages
initial and final velocity to give an average:
where:
vave =
vi = initial velocity
2
vf = final velocity
vave = average velocity
x
These equations apply as scalars or vectors!
It is a good idea to MEMORIZE this formula!
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
Tips:
Check units and do conversions right away
Use as few equations as possible
If solving a multi-part question, avoid using
information from one part to solve another
part (if possible)
vi + vf
Use unrounded values in steps before the
final answer
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
ex. 1: An arrow starts from rest and accelerates
uniformly at 4.0 m/s2 [N]. Find the
velocity after 10 s.
a=
vf - vi
t
vf = vi + at
vf = 0 m/s + (+4.0 m/s2)(10 s) = +40 m/s
= 40 m/s [N]
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
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Kinematics Equations
Kinematics Equations
ex. 2: A helicopter traveling at 20 m/s
accelerates uniformly to a speed of 40
m/s over a distance of 100 m. How long
does it take?
( )
( )
(
)
d=
t=
vi + vf
2
t
t=
2
vi + vf
d
2
100 m = 3.3 s
20 m/s + 40 m/s
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
ex. 3: The initial velocity of an apple is 8.0 m/s
[down] and it accelerates for 3.0 s at 5.0
m/s2 [down].
b) Find the final velocity.
vf - vi
vf = vi + at
a=
t
vf = (-8.0 m/s) + (-5.0 m/s2)(3.0 s)
= -23 m/s = 23 m/s [down]
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
ex. 3: The initial velocity of an apple is 8.0 m/s
[down] and it accelerates for 3.0 s at 5.0
m/s2 [down].
a) Find the displacement.
d = vit + ½at2
= (-8.0 m/s)(3.0 s) + ½(-5.0 m/s2)(3.0 s)2
= -46.5 m = 47 m [down]
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
ex. 4: A cart initially at rest is accelerated
uniformly to a speed of 50 m/s in 30 s.
a) Find the acceleration.
vf - vi
50 m/s – 0 m/s
a=
=
t
30 s
= 1.7 m/s2
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
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Kinematics Equations
Kinematics Equations
ex. 4: A cart initially at rest is accelerated
uniformly to a speed of 50 m/s in 30 s.
b) Find the distance traveled.
d=
( ) (
vi + vf
2
t=
)
0 m/s + 50 m/s
(30 s)
2
= 7.5 x 102 m
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
ex. 5: A car starts at rest, accelerates uniformly
over a displacement of 50 m [E] in 4.0 s.
b) Find the final velocity.
vi + vf
2d
d=
t
vf =
- vi
2
t
2(+50 m)
vf =
- 0 m/s = +25 m/s
4.0 s
= 25 m/s [E]
( )
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
ex. 5: A car starts at rest, accelerates uniformly
over a displacement of 50 m [E] in 4.0 s.
a) Find the acceleration.
2d – 2vit
d = vit + ½at2
a=
t2
2(+50 m) – 2(0 m/s)(4.0 s)
a=
(4.0 s)2
= +6.3 m/s2 = 6.3 m/s2 [E]
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
ex. 6: Superman soars through the air at an
initial speed of 10 m/s towards Lex
Luther, 8500 m away. If he accelerates
at 1000 m/s2, what is his final speed?
vf2 = vi2 + 2ad
vf2 = (10 m/s)2 + (2)(1000 m/s2)(8500 m)
vf = (10 m/s)2 + (2)(1000 m/s2)(8500 m)
= 4.1 x 103 m/s
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
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Kinematics Equations
ex. 7: A cat traveling at 3.0 m/s is chased by a dog
traveling at 3.5 m/s. If the cat has a 100 m
headstart, how long does it take for the dog
to catch the cat?
Since the cat and dog are traveling in the
same direction, the dog is catching up by
the difference between their speeds.
t=
d
vave
=
100 m
3.5 m/s – 3.0 m/s
= 2.0 x 102 s
Kinematics Equations
ex. 8: A train is traveling East at 35 m/s. Another
train on the same track travels West at 78
m/s. They are separated by 1500 m. How
long do dispatchers have to avert a disaster?
Since the two trains travel in opposite
directions, they are closing the distance by
the addition of their speeds.
d
t=
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
vave
=
1500 m
35 m/s + 78 m/s
= 13 s
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
Kinematics Equations
Kinematics Equations
ex. 9: While driving his car, Mr. Jones sees an
obstruction 40 m ahead in the road. It takes
him 0.80 s to react and put his foot on the
brake. His car is traveling at 25 m/s.
ex. 9: While driving his car, Mr. Jones sees an
obstruction 40 m ahead in the road. It takes
him 0.80 s to react and put his foot on the
brake. His car is traveling at 25 m/s.
a) How far does the car travel before he put
his foot on the brake?
b) If the car decelerates at 10 m/s2, will Mr.
Jones hit the obstruction?
vf2 – vi2
d = vavet = (25 m/s)(0.80 s) = 20 m
(we can use this equation because there is
no acceleration during the first movement)
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
d=
vf2 = vi2 + 2ad
(0
d=
m/s)2
-(25
m/s)2
(2)(-10 m/s2)
= 31 m
2a
Since 51 m is needed
to stop, Mr. Jones wil
hit the obstruction!
Dulku – Physics 20 – Unit 1 (Kinematics) – Topic F
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