One dimensional motion - Distance and displacement

One-dimensional motion - Distance and displacement

Jhoan M. Gaviria M.

Objective: To review some terms that are used to describe the motions of objects.

Kinematics

is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Kinematics is a branch of mechanics. The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.

Kinematics

The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In physics, we use these words and many more.

Kinematics

We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration. As we will soon see, these words are associated with mathematical quantities that have strict definitions. 

Scalars and vectors

The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions:

Scalars and vectors

Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

Vectors are quantities that are fully described by both a magnitude and a direction.

Multiple Select

Choose all the scalar quantities

• 20 degrees Celsius

• 30 m/sec, East

• 4000 Calories

• 5 km, North

Multiple Select

Choose all the vector quantities

• 20 degrees Celsius

• 4000 Calories

• 5 km, North

• 30 m/sec, East

Distance and Displacement

Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Distance and Displacement

Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.

Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position and can be calculated as  $\Delta x\ =\ x_f-x_i$ 

Exercise

The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Multiple Choice

Use the diagram to determine the distance traveled by the skier during these three minutes.

• 180 m

• 320 m

• 420 m

• 140 m

Multiple Choice

Use the diagram to determine the resulting displacement traveled by the skier during these three minutes.

• 180 m, rightward.

• 320 m, rightward.

• 420 m, rightward.

• 140 m, rightward.

Exercise

As a final example, consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

Multiple Choice

What is the coach's resulting distance of travel?

• 95 yards

• 55 yards

• 75 yards

• 85 yards

Multiple Choice

What is the coach's resulting displacement of travel?

• 95 yards, left.

• 55 yards, left.

• 75 yards, left.

• 85 yards, left.