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How to Solve Kinematics Problems
There are several steps, an algorithm or recipe, needed to solve any kinematics problem.
1.
READ THE PROBLEM CAREFULLY!!!! This means that you must ask yourself a lot
of questions as you read, so you can interpret the situation described.
a.
The first question you must ask, “What type of motion is this situation about;
constant velocity or constant acceleration?”
Determining the answer is pretty easy. In the textbook the word acceleration or
deceleration often shows up which is a pretty good give away. However, I prefer
not to do this with my problems as in the real world you may not be told so
clearly. Instead I will often describe a situation where the velocity is one value
and later on some new value. If this “change in velocity” happens over a known
distance OR known time then you have CONSTANT ACCELERATION.
Another important clue is if the motion appears to happen over a great distance or
time. If that is the case you have CONSTANT VELOCITY. In other words
accelerations in real life happen over short distances (maximum of a couple of
hundred metres) or short intervals (0 - 90 seconds).
Why is this question of the main importance? If your answer is constant velocity
then the only equation you may use to solve the problem is:
Δx = v x Δt
If your answer is constant acceleration then would not use the above equation but
rather one or more of the following equations:
Δx = v0 x Δt + 1 2 ax Δt 2
Δy = v0 y Δt + 1 2 a y Δt 2
vx = v0 x + a x Δt
v y = v0 y + a y Δt
vx2 = v02x + 2ax Δx
v y2 = v02y + 2a y Δy
In the case of free fall a y becomes g = -9.81m/s 2
Of course the preceding comment is ignoring the mean speed theorem, but it is
not always advisable to do use this starting out.
Read the following practice exercise and determine what type of motion is
described, constant velocity or constant acceleration.
i.
Practice 1: A jumbo jet flies from St. John’s to London Heathrow a
distance of 4500 km at a steady 530 km/h. How long does this flight last?
(ANSWER at the end of the document)
ii.
Practice 2: A jumbo jet takes off from St. John’s International Airport.
Starting from rest it reaches its take off speed of 36.0 m/s over 1200
metres of runway. How long does this take?
(ANSWER at the end of the document)
2.
Next you need to draw a diagram listing the physical quantities you know and do not
know. The physical quantities are displacement, some times expressed as positions,
interval times, initial velocity, final velocity and acceleration.
The diagrams are really just number lines with critical points noted. Such points include
the Start, End and any point in between where the motion changes or you know
additional data.
Why a diagram and not just a “list of knowns and unknowns” as “we did in high school?”
There are two main reasons. First the diagram can act as tool to help you really
understand what is described in the problem. Secondly the list technique lends itself to
“text book problems” not real world situations.
I will illustrate the previous examples.
i.
Practice 1: A jumbo jet flies from St. John’s to London Heathrow a
distance of 4500 km at a steady 530 km/h. How long does this flight last?
ii.
Practice 2: A jumbo jet takes off from St. John’s International Airport.
Starting from rest it reaches its take off speed of 36.0 m/s over 1200
metres of runway. How long does this take?
3.
Time to read again, but this time is not so bad. What is the first thing you are asked to
find, determine or solve for? We see that for both examples the interval time ()t) is the
specific quantity you are asked to solve for.
4.
Knowing what you are looking for consult with your list of equations and find equations
that contain this unknown. Then ask yourself
a.
if you know the rest of the values of the terms in that equation, then your set solve
the problem.
b.
if you do not know two or more terms see if there is another equation that you
know everything but the unknown
c.
if you cannot find such an equation this means you must do an intermediate
calculation to find another unknown, then try to determine the unknown you
initially set out to find.
Remember point (1a)? Your answer there will automatically restrict the equations you
are allowed to use. Bear this in mind when selecting equations.
i.
Practice 1: A jumbo jet flies from St. John’s to London Heathrow a
distance of 4500 km at a steady 530 km/h. How long does this flight last?
Looking for )t and this is constant velocity. This means that I can only use the:
Δx = v x Δt
equation to solve this problem.
Δx = v x Δt
Δt =
Δx 4500km
=
= 8.49h
vx
530 km h
ii.
Practice 2: A jumbo jet takes off from St. John’s International Airport.
Starting from rest it reaches its take off speed of 36.0 m/s over 1200
metres of runway. How long does this take?
We are trying to find interval ()t). Consulting with the appropriate acceleration equations there
are only two that can solve for interval time.
Δx = v0 x Δt + 1 2 a x Δt 2
vx = v0 x + a x Δt
While we know displacement ()x), initial velocity (v0x) and final velocity (vx), we don’t know
acceleration (ax). Therefore, we must first solve for acceleration using the other acceleration
equation.
vx2 = v02x + 2ax Δx
2
2
vx2 − v02x (35.0 − 0 ) m
=
ax =
2 Δx
2(1200)m
2
s2
= 0.51 m s 2
Now we can pick the easiest remaining equation to solve for interval.
vx = v0 x + a x Δt
Δt =
vx − v0 x (35.0 − 0) m s
=
= 68.57 s
0.51 m s 2
ax
Practice 1: A jumbo jet flies from St. John’s to London Heathrow a distance of 4500 km at a
steady 530 km/h. How long does this flight last?
Constant velocity, because this trip is over a very large distance and should have a very
long duration. Real objects only accelerate for very short distances and intervals.
Practice 2: A jumbo jet takes off from St. John’s International Airport. Starting from rest it
reaches its take off speed of 36.0 m/s over 1200 metres of runway. How long does this take?
Constant acceleration, the jet should start with no velocity but after travelling a short
distance of 1200 metres has a positive velocity. This means velocity has changed which
is the event that defines acceleration!