1.Consider the average speed of a runner who jogs around a track four times. The distance (400m) remains constant for each lap.

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3 years ago

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1.Consider the average speed of a runner who jogs around a track four times. The distance (400m) remains constant for each lap.

However, each lap is run 5 seconds slower than the first. The time for each lap increases. The average speed for each lap ______________. This is an example of a(n) _____________ relationship.
A) increases, direct
B) decreases, direct
C) increases, inverse
D) decreases, inverse

Larry and Balky set up an experiment to analyze the motion of a marble as it rolled down an incline. They started the marble at the top of the ramp and set up photogates to collect data as the marble rolled down the ramp.

Which graph format will allow Larry and Balky to calculate instantaneous accleration from the slope of the graph?
A) Velocity on the y-axis, time on the x-axis
B) Distance on the y-axis, time on the x-axis
C) Time on the x-axis, distance on the y-axis
D) Velocity on the y-axis, distance on the x-axis

Tim drives to his brother Casey's house. Given the distance travelled and the time spent, what can Tim calculate about his trip?
A) acceleration
B) density
C) force
D) velocity

Car A travels from New York to Miami at 25 m/s. Car B travels from New York to Chicago, also at 25 m/s.
Car A and Car B have ___________ speeds and ____________ velocities.
A) equal, equal
B) equal, different
C) different, equal
D) different, different
28)
While Bob is demonstrating the gravitational force on falling objects to his class, he drops an 1.0 lb bag of feathers from the top of the science building. Determine the distance the bag has traveled after falling for 1.5 seconds assuming it has reach free fall and given the gravitational acceleration of 9.8 m/sec2.
A) 7.4 m
B) 11 m
C) 15 m
D) 22 m
29)
A boat is travelling down stream in a river at 20 m/s south. A passenger on the boat walks toward the back of the boat at 10 m/s north. Relative to the ground, at what velocity is the passenger moving?
A) 10 m/s north
B) 10 m/s south
C) 30 m/s north
D) 30 m/s south

Sarah wanted to know the velocity of an airplane traveling from Houston to Dallas. After recording the distance (in miles) and time (in hours) it took to travel to Dallas, what other measurement does Sarah need to determine the airplanes velocity?
A) acceleration
B) direction
C) force
D) inertia
33)
If an object is said to be moving at 10 m/s due north. The measurement 10 m/s north would be best described as
A) a speed.
B) a velocity.
C) neither a speed or velocity.
D) either a speed or a velocity.

While performing an experiment, the student creating the data table is not sure if a measurement from the experiment is a vector or scalar. Which question should she ask to determine if a measurement is a vector or a scalar?
A) Is the measurement a rate?
B) Is the measurement in metric units?
C) Does the measurement include direction?
d) Does the measurement include magnitude?

Mathematics

2 answers:

kupik [55] · Answer 1 · 2022-03-14T04:31:12+03:00

1. D) decreases, inverse

The average speed for each lap is given by:

$v=\frac{S}{t}$

where S is the length of the lap (400 m) while t is the time taken to complete the lap. Since the time t increases at each lap, we see from the formula that v, the speed, decreases at each lap. This is an example of inverse relationship: when one of the two quantities increases (the time), the other one decreases (the speed).

2. A) Velocity on the y-axis, time on the x-axis

Acceleration is defined as the change in velocity divided by the time taken:

$a=\frac{\Delta v}{\Delta t}$

In a graph, the slope of a line is given by the increment in y divided by the increment in x:

$s=\frac{\Delta y}{\Delta x}$

Therefore, if we put velocity on the y-axis and time on the x-axis, we immediately see that the acceleration corresponds to the slope of the curve.

3. D) velocity

In fact, velocity consists of 1) speed and 2) direction. The speed can be calculated as:

$v=\frac{S}{t}$

where S is the distance covered and t the time taken. So, by knowing these two quantities, Tim can calculate the speed of the trip. Tim also knows the direction of motion, so he can determine the velocity of the trip.

4. B) equal, different

The difference between speed and velocity is simple: speed is a scalar, and it is just the magnitude of the velocity, so "how fast" is the object moving, while velocity takes also into account the direction of motion, so it is a vector.

Therefore: the two cars have same speed (25 m/s), but they have different velocities, since they are moving into different directions (car A is moving from NY to Miami, while car B is moving from NY to Chicago).

28. B) 11 m

The distance travelled by the bag in free fall is given by:

$S=\frac{1}{2}at^2$

where $a=9.8 m/s^2$ is the acceleration of gravity and t=1.5 s is the time. Replacing these numbers into the formula, we find

$S=\frac{1}{2}(9.8 m/s^2)(1.5 s)^2 =11 m$

29. B) 10 m/s south

The boat is moving 20 m/s south, relative to the ground. The passenger is moving 10 m/s north, relative to the boat. Considering south as positive direction, the passenger's velocity relative to the ground is

$v' = v_b + v_p = 20 m/s + (-10 m/s) = 10 m/s$

and the positive sign means it is due south.

30. B) direction

In fact, velocity is a vector, so it consists of a magnitude (the speed) and a direction. The speed can be determined by the distance and the time, in fact speed is defined as

$v=\frac{d}{t}$

where d=distance and t=time; however, in order to determine velocity, we also need to know the direction of motion.

33. B) a velocity.

In fact, velocity is a vector, and it consists of a magnitude (the speed) and a direction. In this case, 10 m/s is the speed, while north is the direction.

34. C) Does the measurement include direction?

As stated in the previous question, a vector includes both magnitude and direction, while a scalar includes only a magnitude. Therefore, by asking if the measurement includes a direction, we are able to determine if the quantity is a vector or not.