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F AC U L T Y O F E D U C AT I O NF AC U L T Y O F E D U C AT I O N D e p a r t m e n t o f C u r r i c u l u m a n d P e d a g o g y
F A C U L T Y O F E D U C A T I O N
Retrieved from http://www.physics4kids.com/files/art/motion_vector1_240x180.gif
Which of the following are vector quantities?
i.The velocity of a frisbee
ii.The width of a crater made by an asteroid
iii.The speed of a car on the highway
iv.The displacement of a billiard ball after it is struck by the cue ball
A. i only
B. i and ii
C. ii and iii
D. i and iv
E. ii and iv
Answer: D
Justification: A vector quantity indicates that the number has a magnitude (size) and direction. Using this knowledge to answer i through iv it can be determined that:
i the velocity of a frisbee is a vector quantity because the velocity indicates magnitude and direction
ii. the width of a crater made by an asteroid is not a vector quantity because the width does not indicate direction
iii. the speed of a car on the highway is not a vector quantity because the speed of a car does not indicate direction
iv. the displacement of a billiard ball after it is struck by the cue ball is a vector quantity because the displacement indicates magnitude and direction
Answer: C
Justification: A vector quantity always has a magnitude (size) and direction. A scalar quantity only has magnitude. Let us look at each term separately:
Velocity has both a speed and direction. For example, if a car is travelling at 15 m/s to the south, its speed is 15 m/s and its direction is south.
Displacement indicates both distance and direction. For example, if a sack is dropped to the ground from 10 m above the ground, the distance it travelled was 10 m, and the direction was vertically down towards the ground.
Energy has magnitude , but has no direction. It is a scalar, not a vector. For example, a ball travelling north at 10 m/s and a ball travelling south at 10 m/s have the same amount of kinetic energy.
Work results when a force acts upon an object to cause a displacement. The formula for work is: Work = Force × Displacement × Cosine(θ), where θ is the angle between the Force and Displacement vectors. Note that when θ = 90º the result will be zero (cos90º = 0). In other words when Force and Displacement are perpendicular, the force does no work on the body! Work is a scalar product with only magnitude , and NO direction. The SI unit of work is the joule (which is also used for Energy). Work can also be thought of as the change in Energy , and since Energy is a scalar so is Work.
Weight of an object is the force of gravity exerted on that object. It is equal to mass times the acceleration due to gravity. The direction of this acceleration is towards the center of the Earth (or other planet/moon). Therefor weight has both magnitude and direction , and is a vector.
Power is the rate of doing Work. It is equivalent to an amount of Energy consumed per unit time (Joules per second). Since Work and Energy are scalars, we know that Power must also be a scalar. It only has magnitude , and no direction.
Force has both magnitude and direction , and is a vector. It is defined as the mass of an object multiplied by its acceleration. Since acceleration is a vector with a direction, then Force also has direction.
Therefore the answer is C
Answer: C
Justification: Displacement is a vector quantity that refers to an object’s overall change in position. It is the distance from the start to the end point(which in this case would be from P to Q), the path taken does not matter. Since we are asking here for the magnitude of the displacement, we are not required to specify the direction.
If we look at the diagram, we can see that the distance from P to X is 10 m. The distance from X to Q is the diameter of the semicircle. Since the radius of the circle is 5 m, we know that the diameter must be twice the size, therefore 10 m.
So the distance from P to Q = 10 + 10 = 20 m So the answer is C
Extra information:
If we wanted to calculate the distance that Steve travelled, we would need to calculate the circumference of the semi-circle that he travelled along (distance XQ). We can use the equation for the circumference of a circle: Circumference = 2 × π × radius
In this case, since it is a semi-circle we only need to find out half the circumference. So we get:
XQ = π × radius = π × 5 = 15.7 m
To get the total distance we add up the distance PX (10 m) and XQ (15.7) to get 25.7 m
Answer: D
Justification: In order to answer this question we need to draw the vectors that represent Susan’s activities for the day:
Susan’s House High School
Grocery Store^ Elementary School
North
West East
South
15 km
15 km
? km 10 km
We can see that Susan’s path forms a perfect rectangle, and that the last trip she made home from the grocery store must be 10km
We need to remember that distance is a scalar quantity that refers to how much ground an object has covered during its motion, and that displacement is a vector quantity that refers to how far out of place an object is (the object's overall change in position). Since we are only looking at the magnitude of the displacement vector in this question, the direction does not need to be stated.
We can use the previous diagram to calculate each of the following:
A. The total distance Susan travelled from her house to the elementary school is equal to the distance from Susan’s house to the high school plus the distance from the high school to the elementary school:
Distance = 15 km + 10 km = 25km So A is incorrect
D. The magnitude of the displacement vector from Susan’s house to the grocery store can be calculated if we remember that displacement only takes into account Susan’s starting position and end position (and not what route she took to get from start to end). If Susan started at her house, and ended at the grocery store, then her displacement was only 10 km.
Therefore D is the correct answer
Note: The distance Susan covered from her house to the grocery store was 15 + 10 + 15 = 40 km
Steve is driving in his car to take care of some errands. The first errand has him driving to a location 2 km East and 6 km North of his starting location. Once he completes that errand, he drives to the second one which is 4 km East and 2 km South of the first errand. What is the magnitude of the vector that describes how far the car has traveled from its starting point, rounded to the nearest km?
