Scalars & Vectors (College Board AP® Physics 1: Algebra-Based): Exam Questions

1 hour27 questions
1a
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2 marks

Describe the difference between vector and scalar quantities.

1b
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6 marks

Energy is one example of a scalar quantity.

i) Give three other examples of scalar quantities.

ii) Give three examples of vector quantities.

1c
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3 marks

Two students in class are discussing mass and weight. Student A says that weight is a scalar quantity.

State whether you agree with student A and justify your reasoning.

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2
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4 marks

A drone is programmed to fly 5.0 space km north, then 3.0 space km east, and finally 2.0 space km south to reach its target. The drone maintains a constant speed of 10 space straight m divided by straight s during the entire trip.

Indicate whether the total displacement increment x subscript t o t a l end subscriptof the drone is greater than, less than, or equal to the total distance traveled d subscript t o t a l end subscript.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ increment x subscript t o t a l end subscript space greater than space d subscript t o t a l end subscript‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ increment x subscript t o t a l end subscript space equals space d subscript t o t a l end subscript ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ increment x subscript t o t a l end subscript space less than space d subscript t o t a l end subscript

Justify your reasoning.

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3a
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2 marks
4-1-s-q--q2b-easy-aqa-a-level-physics

Figure 1

The helicopter, shown in Figure 1, is moving horizontally through still air. The lift force from the helicopter’s blades is labelled A

Identify the two forces B and C that also act on the helicopter.

3b
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2 marks

The helicopter is moving at a constant velocity. 

Draw a vector triangle to show this arrangement.

3c
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2 marks

Force B has a magnitude of 25 kN and force C has a magnitude of 40 kN. 

Calculate the magnitude of the force needed to keep the helicopter moving at a constant velocity.

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4
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3 marks
Diagram of forces on a point: tension \(T\) at angle \(\theta\), force \(F = 1.5\) N horizontally, and weight \(W = 2.1\) N vertically downwards.

Figure 1

Figure 1 shows a free-body force diagram for a mass suspended from a hook in the ceiling and pulled to one side by a rope. The forces are in equilibrium.

Draw a vector triangle to determine the magnitude of force T and the angle theta.

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5a
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1 mark
Diagram of a pendulum with three positions: X (left, solid line), Y (centre, dashed line), and Z (right, dashed line) from a fixed point.

Figure 1

Figure 1 shows a simple pendulum which consists of a small sphere that hangs from a string with negligible mass. The top end of the string is fixed. The sphere is pulled to Point X and then released from rest and swings through Point Y to Point Z where it changes direction and swings back.

Draw on Figure 1 the velocity vectors at positions X, Y and Z.

5b
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1 mark

On figure 1, draw the acceleration vector at positions X, Y and Z.

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1a
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4 marks

A hiker follows a path consisting of three segments:

  • x with rightwards arrow on top subscript 1 space equals space 4.0 space km due east from initial position x with rightwards arrow on top subscript 0

  • x with rightwards arrow on top subscript 2 space equals space 3.0 space km due north from position x with rightwards arrow on top subscript 1

  • x with rightwards arrow on top subscript 3 space equals space 2.0 space km due west from position x with rightwards arrow on top subscript 2

The hiker maintains a constant average speed of 1.5 space straight m divided by straight s while walking.

Estimate whether the hiker's average velocity is greater than, less than, or equal to their average speed.

Justify your estimate using qualitative reasoning.

1b
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2 marks

Determine an expression for:

i) the hiker’s average speed in terms of d and t.

ii) the magnitude of the hiker's average velocity in terms of x, y and t.

1c
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3 marks

Does the expression you derived in part b) support your qualitative reasoning from part a)? Justify qualitatively why or why not.

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2
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4 marks

A skier moves down an inclined plane with an angle theta space equals space 30 degree relative to the horizontal. The skier's initial velocity at the top of the incline is 5.0 space straight m divided by straight s, and air resistance is negligible.

i) Draw a labeled diagram showing the skier’s velocity vector at the start and its components relative to the incline.

ii) Determine expressions for the initial velocity components parallel and perpendicular to the incline in terms of v subscript 0.

iii) Calculate the horizontal and vertical velocity components of the skier.

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3
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5 marks

Two students set up an investigation measuring how distance from the pivot point affects torque. The students use a hinged door in their investigation.

Student A makes the following claim:

"Since torque is measured in newton-meters, torque is equivalent to the work done by the force on the door."

Identify whether Student A is correct or incorrect.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ correct, ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ incorrect.

Justify your answer using qualitative reasoning.

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4
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2 marks

A transatlantic airplane cruises at a constant velocity of 150 space straight m divided by straight s heading from New York to London. Some time later, a tail wind develops and the cruising velocity increases to 200 space straight m divided by straight s.

Draw the relative cruising velocities as vectors and indicate the scalar multiplication factor.

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5a
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2 marks
Diagram showing a boat on a river between north and south banks, with copyright text "Save My Exams" in the background.

Figure 1

A boat moves 5.0 space straight m divided by straight s due north relative to the water, while the river current flows 3.0 space straight m divided by straight s due east.

On the diagram in Figure 2, draw and label arrows to represent the components of the boat's velocity vectors relative to an observer on the riverbank. Clearly indicate the boat’s velocity relative to the water, the river’s velocity, and the boat’s resultant velocity.

The boat from the diagram Figure 1

Figure 2

5b
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4 marks

i) Derive an expression for the magnitude of the boat’s velocity relative to the riverbank in terms of v subscript x and v subscript y. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.

ii) Calculate the magnitude and direction of the boat’s velocity relative to the riverbank, measured counterclockwise from due east.

5c
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4 marks

In a second trip, the boat crosses the river further downstream, where the velocity of the river is 1.5 space straight m divided by straight s. The distance between the north and south banks is equal at both locations, and the boat's speed relative to the water remains the same.

Indicate whether the boat’s crossing time in this case would be greater than, less than, or equal to the time taken in the original scenario.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ t subscript n e w end subscript space greater than space t subscript o r i g i n a l end subscript‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ t subscript n e w end subscript space equals space t subscript o r i g i n a l end subscript ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ t subscript n e w end subscript space less than space t subscript o r i g i n a l end subscript

Justify your reasoning.

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1a
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3 marks

A boat is trying to cross from the south bank to the north bank of a river that is 152 space straight mwide while a current flows 3.22 space straight m divided by straight s eastward relative to the river bank. The boat moves at 4.19 space straight m divided by straight s relative to the water and must reach a point directly across from its starting position.

Draw a labelled vector diagram representing the boat’s velocity from the reference frame of an observer on land.

1b1 mark

Determine the angle at which the boat must be aimed to arrive at its intended final position.

1c
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2 marks

i) Determine the time required for the boat to cross the river.

ii) If the boat is instead aimed directly across the river, estimate how far downstream it will drift before reaching the other side.

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2
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5 marks

The following data shows the position of a drone relative to the person controlling it, at specific moments during its flight.

Time (s)

x, y, z position (m)

0.0

(0, 0, 0)

2.0

(2, 3, 0)

4.0

(6, 3, 5)

6.0

(6, 7, 10)

8.0

(3, 10, 15)

10.0

(-2, 5, 7)

Describe the motion of the drone.

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