Scalars and Vectors
What makes up a scalar quantity?
A numerical value and a unit
Define distance and displacement and explain the difference between the two
Distance is the magnitude of the total path traveled and displacement is the change in position.
Distance is a scalar quantity and displacement is a vector quantity.
Define average speed and average velocity and explain the difference between the two.
Average speed is the rate of change of distance (distance traveled over time) and average velocity is the rate of change of displacement (change in position over time).
Speed is a scalar quantity and velocity is a vector quantity.
What goes on the vertical and horizontal axes of a position-time graph? Which one is the independent variable?
Position on the vertical axis (m)
Time on the horizontal axis (s)
Time is the independent variable (position is a function of time)
What makes up a vector quantity?
A numerical value and a unit (magnitude) and a direction
Consider an objects motion from one point to another. What must first be defined in order to determine the object's displacement vector?
A coordinate system/frame of reference
Britta Steffen of Germany set the women's Olympic record for the 100.0 m freestyle swim with a time of 53.12 s. What was her average speed? Give your answer in m/s and km/h.
1.883 m/s
6.777 km/h
What do the slope and intercept of a position-time graph represent? How do you find each for a straight line?
Slope = average velocity
Intercept = initial position
Slope = v = rise/run = (x2 - x1)/(t2 - t1)
Intercept = x1 - v*t1
Name an example of 3 scalar quantities and 3 vector quantities
Scalar: distance, speed, mass
Vector: displacement, velocity, acceleration
Given an initial position and a final position, how many possible displacements between the points can you define? How many possible distances traveled between the points?
Only one possible displacement can be defined
Infinitely many distances can be defined
In what case (if any) are the following true:
A. the average speed of an object's motion is equal to the magnitude of its average velocity
B. the average speed of an object's motion is greater than the magnitude of its average velocity
C. the average speed of an object's motion is less than the magnitude of its average velocity
Draw a sketch to support your answer
1. when the distance is equal to the displacement (the path traveled is the shortest straight line distance between the initial and final positions)
2. when the distance is greater than the displacement (a path was traveled other than the shortest straight line distance between the initial and final points)
3. Never
What do positive, negative, and zero slopes mean on a position-time graph? When comparing speeds of two position-time graphs what do you look at? When comparing velocities what do you look at?
positive slope means positive velocity (motion in the positive direction), negative slope means negative velocity (motion in the negative direction), and zero slope means zero velocity (no motion/ at rest)
When comparing speeds look at how steep the slopes are. Steeper slope means greater speed (regardless of positive or negative).
When comparing velocities look at both steepness and positive/negative.
What is the meaning of a resultant vector?
A resultant vector is the vector that RESULTS from any number of vector operations (e.g. adding two or more vectors).
Consider that you are given a description of an objects motion in one direction (e.g. traveled 5 m West, then 8 m East, then another 12 m West). Explain how to find the resultant displacement vector graphically and mathematically?
1. Define a coordinate system/ frame of reference
Graphically:
2. Draw each of the vectors corresponding to each displacement with the tip of the first vector touching the tail of the second vector and so on.
3. The resultant vector is begins at the tail of the first vector and ends at the tip of the final vector that was added.
Mathematically:
Using the defined coordinate system, add the displacements with their appropriate magnitudes and directions (for 1D, this would be positive and negative signs)
You drive your car in a straight line at 15.0 m/s for 10.0 km, then you drive back to your starting point at 25.0 m/s. What is your average speed for the whole trip? What is your average velocity?
Show your work on the board.
Average velocity is zero since the displacement is zero
Average speed is 18.8 m/s
What is the difference between instantaneous and average velocity? When are they the same? Draw a sketch of a position-time graph to support your answer
Average velocity is the change in position over a finite time interval. Instantaneous velocity is the velocity at an instant of time.
They are the same when the velocity is constant (straight line).
They are different when the velocity is not constant. In that case, instantaneous velocity is the slope of the tangent line to the position-time curve.
How can you find the components (in two directions) of a vector given its magnitude and its direction?
You can use trigonometry (sin, cos) to RESOLVE the vector into its components.
rx = rcos(theta)
ry = rsin(theta)
What are the magnitude and the direction of the resultant displacement of an object that moves 5.0 m North and then 6.0 m West? Draw a sketch to support your answer
magnitude = 7.8 m
direction = 50. degrees West of North
You jog at 9.50 km/h for 8.00 km; then you jump into a car and ride an additional 16.0 km. What average speed must the car have for the average speed for the entire 24.0-km trip to be 22.0 km/h?
Show your work on the board.
t1 = 0.842 hour
t2 = 0.2488 hour ~0.25 hour
v2 = 64 km/h
A soccer ball rests on the field at the location x = 5.0 m. Two players run along the same straight line toward the ball. Their equations of motion are as follows:
x1 = -8.2 m + (4.2 m/s)t
x2 = -7.3 m + (3.9 m/s)t
Which player is closer to the ball at t = 0 s?
At what time does one player pass the other?
Player 2
t = 3.0 s