How to solve Kinematics exercises?

Check out some tips to solve a good part of the Kinematics exercises:

1. Good interpretation: Reading is essential for understanding a Kinematics problem. Sometimes it will be necessary to read the exercise more than once to fully understand the problem. Over time, you will notice that some important exercise variables are implicit in the text or in graphics or even figures. See examples:

Example 1

a body starts from rest.

In this sentence, it is implied that the initial velocity of the body was equal to 0 (v₀ = 0) and that it has undergone some change, indicating the existence of an acceleration. It is possible to infer, in this case, that its movement is uniformly variable.

Example 2

A car, moving at 20 m/s, brakes to a complete stop.

Analyzing the sentence, we realized that the initial velocity of the body was equal to 20 m/s (v₀ = 20 m/s) and that the car's final speed is 0, as it stops completely (v_f = 0 m/s). As its initial velocity is positive and decreases with time, we infer that it moves away from the observer and the at the same time it slows down, so it is a uniformly varied, progressive and retarded.

2. Always write down exercise data:Always write down all the variables the exercise provides, as well as all the ones it asks you to calculate or that you haven't told me about but are important to solving the problem. See an example:

A driver, driving on a road at 108 km/h, sees a stop sign and then applies his vehicle's brakes, coming to a complete stop 6 s after the start of braking. Calculate the modulus of the average acceleration, in m/s², suffered by the vehicle from braking.

Data:

v₀ = 108 km/h – initial speed
v_f = 0 m/s – final speed
Δt = 6 s - time interval
The_m =? – average acceleration (unknown)

3. Check the units:Units must always be compatible with each other, that is, they must all be represented in the same unit system. The International System of Units uses the standard subway and second for distances and time intervals, respectively. Thus, the speed must be given in m/s. Check out some useful transformations:

1 kilometer = 1 km = 10³ m = 1000 m

1 centimeter = 1 çm = 10^-2 m = 0.01 m

1 kilometer per hour = 1 km/h = 3.6 m/s (meters per second)

1 mile per hour = 1 mph = 0.44704 m/s (meters per second)

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Note that in the example shown in item 2, we have a unit mismatch and therefore we must convert the 108 km/h in m/s dividing by 3,6.

See too: How to solve exercises on Newton's laws?

4. Get to know the equations of motion: Uniform motion, that is, motion without acceleration, has only one equation. Accelerated motion has four equations that can be used in different situations. Check out:

Average speed: It is the equation used for uniform motion, that is, motion whose velocity is constant. In this type of movement, the body moves equal spaces at equal time intervals. See the same equation written in two different ways:

v_m = S
t

or

s_f = S₀ + v_m.t

Subtitle:

s₀ = starting position
s_f = final position
ΔS = S_f - S₀ – Displacement
v = Average speed
t = Time interval

average acceleration: It is the equation used for uniformly varied motion, that is, motion whose speed varies constantly. In this type of movement, the body changes its speed in equal proportions during equal intervals of time. See the same equation written in two different ways:

THE_m = ov
t

or

v_f = v₀ + A_m.t

Subtitle:

v₀ = initial speed
v_f = Final speed
Δv = v_f -v₀ – speed variation
THE_m = Average acceleration
t = Time interval

Position time function: This is the equation used when we need to find the displacement or the final and initial position of a mobile moving with constant acceleration. See the same equation written in two different ways:

ΔS = v₀.t + THE_m.t²
2

s_f = S₀ + v₀.t + THE_m.t²
2

Subtitle:

s₀ = starting position
s_f = final position
ΔS = S_f - S₀ – Displacement
v₀ = initial speed
THE_m = Average acceleration
t = time interval

Torricelli Equation: This equation is similar in use to the equation shown above, however, it can be very useful when the exercise statement does not report the time at which the movement occurred. Watch:

v_f ²=v₀² + 2.A_m.ΔS

Subtitle:

v_f= final speed
ΔS = S_f - S₀ – displacement
v₀ = initial speed
THE_m = average acceleration
By Rafael Hellerbrock
Graduated in Physics

Would you like to reference this text in a school or academic work? Look:

HELERBROCK, Rafael. "How to solve Kinematics exercises?"; Brazil School. Available in: https://brasilescola.uol.com.br/fisica/como-resolver-exercicios-cinematica.htm. Accessed on June 27, 2021.