Part I: Scalar and Vector Quantities

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Presentation transcript:

Part I: Scalar and Vector Quantities Intro to Kinematics Part I: Scalar and Vector Quantities

Kinematics -The mathematical treatment of the motions of bodies without regard to the forces that produce the motion. (i.e. one-dimensional motion, free-fall, 2D motion)

Scalar Quantity -A Scalar quantity has magnitude but NOT direction Examples: Distance Time Speed Mass Temperature Energy

Vector Quantity -A Vector quantity has BOTH magnitude and direction (ex. 50 meters North) Examples: Displacement Acceleration Force Momentum Electric Force Magnetic Force

Let’s try a few examples on your note sheet… Answers: a. vector b. scalar c. scalar d. vector e. scalar f. vector g. scalar h. vector i. vector j. scalar k. vector

Distance and Displacement Part 2 Distance and Displacement

DISTANCE (Try the next two!) Distance is the TOTAL length of a path that an object travels. Distance is a SCALAR quantity which means it ONLY has magnitude. (Disregard direction!!!) Ex.) Jenny walks 30 meters north, 40 meters south, and 20 meters north. Determine the distance travelled by Jenny. (Try the next two!)

DISPLACEMENT Displacement is the change in the position of an object described by a vector that begins at the initial position of the object and ends at its final position (shortest way from start point to finish). Displacement has BOTH magnitude and direction. Therefore, if a problem asks for displacement, both magnitude and direction must be taken into account. Ex.) Jenny walks 30 meters north, 40 meters south, and 20 meters north. Determine the displacement travelled by Jenny. (Remember direction!!!) For a better understanding: School of Physics--Distance versus Displacement

Pythagorean Theorem and Displacement Many displacement problems will require the use of the Pythagorean Theorem. For these and other displacement problems, a PICTURE will always help. Ex.) An airplane travels 400 meters north and then 300 meters east. Determine the displacement of the airplane.

Now for a tricky one… The city bus travels 5 blocks east, 7 blocks south, and then 2 blocks west. Determine the displacement of the bus.

Part 3 Speed and Velocity

SPEED An object is considered moving when its position changes with time. The SPEED of an object is the distance the object moves per unit of time. Since we are talking about distance and not displacement, speed is a SCALAR quantity. The average speed of an object is given by the following equation:

Facts about speed: The unit for distance is meters (m) and the unit for time is seconds (s) which makes speed have units of m/s. If speed remains the same throughout the time period, the object is said to have constant speed or uniform motion. If the speed varies, the motion is non-uniform.

Speed Problems… (Remember to use distance, NOT displacement. Time is always the same) The school bus covers a distance of 400 meters in 20 seconds. What is the average speed of the bus? Johnny rides his bicycle 40 meters north and 20 meters east in 10 seconds. What is Johnny’s average speed?

Velocity The average velocity of an object is the time rate of change of its DISPLACEMENT. Therefore, velocity is a VECTOR quantity having both magnitude and direction. In velocity problems, make sure you find the displacement first! The average velocity of an object is given by the equation: Pretty much the same equation as before yielding the same units (m/s); only this time you are using displacement (direction matters!!!) Make sure your answer includes direction.

Velocity Problems… Johnny rides his bicycle 40 meters north and 20 meters east in 10 seconds. What is Johnny’s average velocity? A fighter jet flies 3 km west and then 2 km east in 8 minutes. Determine the jet’s average velocity. (Remember to convert!)

Part 4: Acceleration The time rate of change of velocity is acceleration. Acceleration is a vector quantity and is defined as the change of velocity per unit of time. The equation is:

Example: A golf ball starts from rest. A golfer hits the ball and it travels 80 m/s in 5 seconds. Determine the acceleration of the ball.

How about these… A football is thrown 10 m/s and is caught and brought to rest in 4 seconds. Determine the acceleration of the ball. (Be careful with the change in velocity!) A paper airplane has an acceleration of 5 m/s^2. If it is thrown from rest, how fast will it be going in 3 seconds?