Lesson 2.1 Displacement and Velocity Essential Question: How do you calculate the displacement and velocity of an object?

What is mechanics? The branch of physics concerned with motion and forces. The subset of mechanics that describes motion without regard to its causes is called kinematics.

What is motion? Happens all around us Objects move in different directions at different speeds One dimensional motion is the simplest form of motion

What is one-dimensional motion? Motion that happens in one direction. The motion of a commuter train on a straight track Forward or backwards

How is motion described? Displacement Velocity Acceleration

Motion takes place over time and depends upon the frame of reference. One key approach to studying a complex situation is to choose a frame of reference against which you can measure changes in position.

What is a frame of reference? A system for specifying the precise location of objects in space and time. When you select a reference frame, note that it remains fixed for the problem in question and has an origin, or starting point, from which it is measured.

How do I select a frame of reference? Choose one that is used consistently Sometimes, one frame of reference will make explanations easier Think of either the x-axis or y-axis of the coordinate plane

What is displacement? The length of the straight line drawn from its initial position to its final position of any object that is moving from one position to another Displacement is a change in position, ∆𝑥.

How do you calculate displacement? ∆𝑥= 𝑥 𝑓 − 𝑥 𝑖 To find displacement, take the final position and subtract the initial position.

What is distance? Distance is the length moved. It’s a scalar quantity. How far did you travel?

Are displacement and distance traveled the same? NO! Displacement is not always equal to the distance traveled. It’s a description of the direction of the motion.

You leave your house and walk 4 km due east and then turn and walk 3 km due west. What is your distance? What is your displacement?

What sign will displacement have? Positive Traveled to the right or up Negative Traveled to the left or down

Is displacement the complete descriptor of motion? No, displacement doesn’t completely describe the motion of an object. Knowing the speed when evaluating motion is important.

What is average velocity? The total displacement divided by the time interval during which the displacement occurred. The unit of velocity is meters per second, m/s.

How do I calculate average velocity? 𝑣 𝑎𝑣𝑔 = ∆𝑥 ∆𝑡 = 𝑥 𝑓 − 𝑥 𝑖 𝑡 𝑓 − 𝑡 𝑖 average velocity= change in position change in time = displacement time interval

The average velocity can be positive or negative, depending on the sign of the displacement. The average velocity is equal to the constant velocity needed to cover the given displacement in a given time interval.

Average velocity is not always equal to the average of the initial and final velocities. For instance, if you drive first at 40 km/h west and later at 60 km/h west, your average velocity is not necessarily 50 km/h west.

During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s displacement after 137 s?

Heather and Matthew walk with an average velocity of 0.98 m/s eastward. If it takes them 34 min to walk to the store, what is their displacement?

If Joe rides his bicycle in a straight line for 15 min with an average velocity of 12.5 km/h south, how far has he ridden?

It takes you 9. 5 min to walk with an average velocity of 1 It takes you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement?

Simpson drives his car with an average velocity of 48 Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway?

Simpson drives his car with an average velocity of 48 Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway? How much time would Simpson save by increasing his average velocity to 56.0 km/h to the east?

A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then, it travels 210 km south with an average velocity of 75 km/h to the south. How long does the total trip last? What is the average velocity for the total trip?

Car A travels from New York to Miami at a speed of 25 m/s Car A travels from New York to Miami at a speed of 25 m/s. Car B travels from New York to Chicago, also at a speed of 25 m/s. Are the velocities of the cars equal? Explain.

What is speed? A measure of how fast something is moving The rate at which distance is covered

Is Velocity = Speed? Velocity is not the same as speed. Speed is a number without direction. Velocity describes motion with both a direction and a numerical value (a magnitude).

The speedometer of a car moving northward reads 60 km/h The speedometer of a car moving northward reads 60 km/h. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity?

Velocity can be interpreted graphically. The motion of an object moving with constant velocity will provide a straight-line graph of position versus time. The slope of this graph indicates the velocity.

What is needed to interpret velocity graphically? Object’s position at specific times A graph Time plotted on the horizontal axis Position plotted on the vertical axis

When velocity is constant, displacement varies directly with time When velocity is constant, displacement varies directly with time. It’s a linear relationship. The slope of a position-time is the velocity of the object.

What is instantaneous velocity? The velocity of an object at some instant or at a specific point in the object’s path It may not be the same as the average velocity

Consider an object whose position versus time graph is not a straight line, but a curve. The object moves through larger and larger displacements as each second passes. Thus, its velocity increases with time.

We can obtain different average velocities, depending on the time interval we chose.

How do you find an instantaneous velocity? Construct a straight line that is tangent to the position-versus-time graph at that instant. The slope of this tangent line is equal to the value of the instantaneous velocity at that point.

How do you calculate the displacement and velocity of an object?