Kinematics: concept and formulas

In the field of Physics Mechanics, Kinematics studies and describes the movement of bodies without worrying about the causes of displacement.

Through Kinematics it is possible to classify and compare the movements, while the reason for the occurrence is addressed in Dynamics.

fundamental concepts

See below some important concepts in the study of Kinematics.

• Referential: point that determines whether the object is in motion or at rest.
• Movement: change of position to approach or move away from the reference frame.
• rest: when the position of an object does not change in relation to a frame of reference.
• Trajectory: line that determines the different positions of the object over time.
• Displacement: distance traveled between the initial and final space of the trajectory.
• material point: body whose dimensions do not interfere with the study of movement.
• long body: body whose dimensions are important for understanding movement.

Example: A boy inside a car is considered as A and moves to the right towards reference B, which corresponds to a girl standing near the crosswalk.

Since B is the referential, we say that A is in motion in relation to B, that is, it is making a trajectory, as the distance it is from B varies with time. Note that the movement performed by a body depends on the adopted frame of reference.

Path type classifies movement as straight, when the movement is performed on a straight line, or curvilinear, when the movement is performed on a curved path.

Kinematics Formulas

average speed

The speed with which the movement is performed by a body is called average speed, which can be calculated using the following formula:

The initial and final terms correspond to the period of time counting, no matter if the car was stopped for some time or if there was a variation in speed along the route.

In the International System (SI) the average speed unit is the meter per second (m/s).

See too: Kinematics Formulas

medium scalar acceleration

Over time, the speed of a body can change as it moves. The acceleration of a body causes the variation in velocity during a journey to increase or decrease over a given period of time.

Here's the formula for calculating acceleration:

In the International System (SI) the average acceleration unit is the meter per second squared (m/sec²).

See too: Acceleration

Uniform Movement (MU)

If in the same time interval a body always travels the same distance, its movement is classified as uniform. Therefore, its speed is constant and different from zero along the way.

At the Uniform Rectilinear Movement (MRU) the velocity does not change on a trajectory taken in a straight line.

The position of the body on the trajectory can be calculated by the hourly position function:

Where,

S = final position, in meters (m)
s₀ = initial position, in meters (m)
v = speed, in meters per second (m/s)
t = time, in seconds (s)

See too: Uniform Movement

Uniformly Varied Movement (MUV)

If velocity varies by equal amounts over the same time interval, the movement is characterized as uniformly varied. Therefore, the acceleration is constant and non-zero.

O Uniformly Varied Rectilinear Movement (MRUV) is characterized by the same amount of acceleration as a straight-line body.

Through the hourly velocity equation it is possible to calculate the velocity as a function of time.

Where,

V = final velocity, in meters per second (m/s)
V₀ = initial speed, in meters per second (m/s)
a = acceleration, in meters per second squared (m/s²)
t = time, in seconds (s)

The position of the body during the trajectory can be calculated using the following equation:

Where,

S = final position, in meters (m)
s₀ = initial position, in meters (m)
V₀ = initial speed, in meters per second (m/s)
a = acceleration, in meters per second squared (m/s²)
t = time, in seconds (s)

THE Torricelli equation is used to relate velocity and space traversed in uniformly varied motion.

Where,

V = final velocity, in meters per second (m/s)
V₀ = initial speed, in meters per second (m/s)
a = acceleration, in meters per second squared (m/s²)
= space traveled, in meters (m)

See too: Uniformly Varied Movement

Use the exercise lists below to practice using the formulas and gain more knowledge.

• Kinematics Exercises
• Average Speed ​​Exercises
• Exercises on Uniform Movement
• Exercises on Uniformly Varied Movement.