Physics-Kinematics: Objects in Motion: Grade 11

Lesson Objective: Understanding the meaning of kinematics, real-world examples, elements of kinematics, and intro into describing the movement of objects using numbers and equations.

Next Generation Science Standard: Use mathematical representations of phenomena to describe explanations. (HS-PS2-2),(HS-PS2-4)

Materials: This lesson is an introductory lesson to the larger concept of kinematics, more of a lecture than an activity. Prepare projections beforehand that list the kinematic equations and the example. You'll also need:

• A rubber ball
• A toy car

Starter

Ask: Has anyone heard the word "Kinematics" before? (Allow the students to answer.) If yes, great. Can you tell me what it means? (If someone answers correctly, positively reinforce the answer and continue.)

Say: Kinematics is derived from the Greek word Kinesis which means movement. It is generally defined as the study of the motion of points, objects, or groups of objects. In physics, it belongs to a branch called Mechanics. 

Kinematics should not be confused with kinetics. Both concepts are branches of motion and are very similar. However, kinetics is the study of the forces that affect or cause motion (Newton's Laws), such as the way friction affects walking or running or how an enzyme causes changes in a chemical system.

Today, we're discussing kinematics, the science dedicated to an object or substance in motion without considering the forces that stimulate it. A good idea is to think of it as the how and the why. Kinetics considers why the motion happens, and kinematics is concerned with how it happens.

Because kinematics involves a substantial amount of math, we must grasp the basic concepts and terms first to better understand why we are performing the math that we are.

Main

Say: Kinematics is shooting a basketball, water running down from a waterfall, a moving train. Practically any object in existence involves kinematics as long as it's moving. Even a textbook on the table could be an example of kinematics if you consider the vibration of atoms and molecules.

This is the long and short of the theoretical part of kinematics, and basically all there is to it. However, we can translate these words into mathematical expressions called kinematic equations.

There are a couple of elements or quantities that are important to mathematically calculate how movement happens. These elements are vector and scalar quantities. You've probably already heard these terms. Scalar quantities are those that only have magnitude, meaning they are described by a numerical value alone. On the other hand, vector quantities are those that have both magnitude and direction. 

The scalars we'll be considering today are (write on the board):

• speed
• distance
• time

And the vectors are (write on the board):

• displacement
• velocity
• acceleration

Later on, you'll see that all calculations will be focusing on vector quantities.

How exactly do kinematic equations work? Let's take velocity, for instance. Velocity is the rate and direction of movement. So imagine I am throwing a ball into the trash can, and it travels at about 1km/hr. From where I'm standing, it'd be moving eastward into the container.

Do: Throw the ball into the empty trash can.

Ask: Let's say the velocity is simply 1km/hr eastward, right? (Allow the students to answer).

Say: When calculating the velocity of movement, kinematics considers the distance the ball has traveled and the time it took to come to a halt. If we could break this down, this means we're considering the ball's starting point (my hand), ending point (the trash can), and its trajectory (the path it follows through space). This is why physicists often refer to kinematics as the "geometry of motion." Effectively, kinematics studies the trajectories of points, lines, and other geometric objects when calculating motion.

Kinematics isn't just about projectile motion, however. It's also present in vertical and horizontal movement.

Do: Throw the ball straight up in the air and allow it to fall to the floor.

Say: The kinematics here involves the ball's velocity when it goes up, the acceleration (change in velocity) as it comes back down, and the time it takes to come to a halt from the start to the end of motion.

Do: Push the toy car across your desk.

Say: Here as well, we're concerned with the distance between point A and point B, how fast was the car traveled, and changes in velocity along the way.

The next step for us is actually performing the calculations. Fortunately, there are a set of basic formulas that are used to do this.

Do: Project the following information on a screen. Allow time for students to copy the information.

• v = v0 + at
• d = ((v + v0)/2)t
• d = v0t + 1/2at2
• v2 = v02 + 2ad

Keys

• v0 = initial velocity
• v = final velocity
• d = displacement
• a = acceleration
• t = time interval

Say: These formulas are based on the assumption that acceleration is constant and that all parameters or quantities refer to the same direction.

Do: Project the following example.

Say: Now for an example. An airplane moves along a runway at 3.20 m/s2 for 32.8 s until it finally lifts off the ground. Determine the distance traveled before takeoff.

Do: Work through the solution with your students.

The parameters we have are:

• a = 3.20 m/s2
• t = 32.8 s
• v = 0 m/s (the plane was stationary at the start)
• d = ?

Using the formula:

• d = v0t + 1/2at2

We can calculate the distance (displacement) as;

• d = (0 m/s)*( 32.8 s) + 1/2(3.20 m/s2)*( 32.8 s)2
• d = 1721m

Say: As we continue through this section, you'll start to see just how simple it is to apply kinematics to kinetic situations. 

Feedback

Ask: How do you think engineers apply kinematics to something like a plane, car, or other machinery? How would they use these different equations? (Allow students to answer.)

Say: Go home and throw an object across your living room—just don't break anything. Have someone use a timer that goes into the milliseconds. They should start the timer when you release the ball and stop it when it hits the ground. Before you throw the ball, mark your spot on the floor. 

Once the object lands, measure the distance between where you threw the ball and where it landed. From the information you have, calculate how fast the ball traveled through the air. Now, figure out how long that ball would have to be airborne to travel one mile.

We'll discuss your calculations in the next class.

Written by Anne Ifeanyi

Education World Contributor

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