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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 1: KinematicsScalars & Vectors

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

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Scalars & Vectors

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1
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A pilot directs an airplane due north at a speed of 151 space straight m divided by straight s. A prevailing wind blows due east at an average speed of 12.3 space straight m divided by straight s.

Which of the following describes the direction the airplane will fly as a result of the wind?

  • 3 degree space straight E space of space straight N

  • 4 degree space straight E space of space straight N

  • 5 degree space straight E space of space straight N

  • 6 degree space straight E space of space straight N

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2
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A with rightwards arrow on top is a vector quantity. Which of the following statements could be true?

  • A with rightwards arrow on top is velocity. When multiplied by negative 2, the velocity becomes negative 2 A with rightwards arrow on top

  • A with rightwards arrow on top is speed. When multiplied by negative 2, the speed becomes 2 A with rightwards arrow on top

  • A with rightwards arrow on top is weight. When multiplied by negative 2, the weight becomes 2 A with rightwards arrow on top

  • A with rightwards arrow on top is acceleration. When multiplied by negative 2, the acceleration becomes negative 4 A with rightwards arrow on top

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3
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v squared subscript x space equals space v squared subscript x space 0 end subscript space plus space 2 a subscript x space open parentheses x space minus space x subscript 0 close parentheses

The equation above is a kinematic equation.

Which of the following equations is the above equation's correctly derived from?

  • v squared space equals space v squared subscript 0 space plus space 2 a with rightwards arrow on top increment x with rightwards arrow on top

  • v squared space equals space v squared subscript 0 space plus space 2 a increment x

  • v with rightwards arrow on top squared space equals space v squared subscript 0 space plus space 2 a with rightwards arrow on top increment x

  • v with rightwards arrow on top squared space equals space v with rightwards arrow on top squared subscript 0 space plus space 2 a with rightwards arrow on top increment x with rightwards arrow on top

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4
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A car travels 100 m east and then 60 m west.
Which of the following gives the car’s displacement from its initial starting position?

  • negative 60 space straight m

  • negative 40 space straight m

  • plus 40 space straight m

  • plus 160 space straight m

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5
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Two vectors, A with rightwards arrow on top and B with rightwards arrow on top, are represented graphically, with B with rightwards arrow on top placed tip-to-tail with A with rightwards arrow on top. The resultant vector R with rightwards arrow on top is drawn from the tail of A with rightwards arrow on top to the tip of B with rightwards arrow on top.

Which of the following best describes the vector R with rightwards arrow on top?

  • The vector difference between A with rightwards arrow on top and B with rightwards arrow on top.

  • The vector sum of A with rightwards arrow on top and B with rightwards arrow on top, representing their combined effect.

  • The scalar multiplication of A with rightwards arrow on topand B with rightwards arrow on top.

  • A vector perpendicular to both A with rightwards arrow on top and B with rightwards arrow on top.

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1
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The magnitude of vector Z with rightwards arrow on top is 20. Which of the following could be components of vector Z with rightwards arrow on top?

  • Z subscript x space equals space 10, Z subscript y space equals space 2

  • Z subscript x space equals space 10, Z subscript y space equals space 10

  • Z subscript x space equals space 12, Z subscript y space equals space 16

  • Z subscript x space equals space 20, Z subscript y space equals space 20

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2
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open vertical bar P with rightwards arrow on top close vertical bar space equals space open vertical bar Q with rightwards arrow on top close vertical bar

Vector P with rightwards arrow on top has a direction of south, and vector Q with rightwards arrow on top has a direction of west.

Which of the following expressions correctly describes the magnitude and direction of the vector P with rightwards arrow on top space plus space Q with rightwards arrow on top?

  • P with rightwards arrow on top space plus space Q with rightwards arrow on top space equals space 2 open vertical bar P with rightwards arrow on top close vertical bar space SW

  • P with rightwards arrow on top space plus space Q with rightwards arrow on top space equals space 2 open vertical bar P with rightwards arrow on top close vertical bar space NE

  • P with rightwards arrow on top space plus space Q with rightwards arrow on top space equals space open vertical bar P with rightwards arrow on top close vertical bar square root of 2 space SW

  • P with rightwards arrow on top space plus space Q with rightwards arrow on top space equals space open vertical bar P with rightwards arrow on top close vertical bar square root of 2 space NE

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3
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Two forces, stack F subscript 1 with rightwards arrow on top space equals space 10 space straight N at 30 degree above the horizontal and F with rightwards arrow on top subscript 2 space equals space 8 space straight N at 60 degree above the horizontal in the same direction, act on an object.

Which of the following most nearly gives the magnitude of the resultant force acting on the object?

  • 15.6 space straight N

  • 16.1 space straight N

  • 17.4 space straight N

  • 18.5 space straight N

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4
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The magnitude of vector A with rightwards arrow on top is 5.

Which of the following could be the magnitude of the horizontal and vertical components of vector A with rightwards arrow on top?

  • stack A subscript x with rightwards arrow on top space equals space 3 and stack A subscript y with rightwards arrow on top space equals space 2

  • stack A subscript x with rightwards arrow on top space equals space 3 and stack A subscript y with rightwards arrow on top space equals space 4

  • stack A subscript x with rightwards arrow on top space equals space 5 and stack A subscript y with rightwards arrow on top space equals space 5

  • stack A subscript x with rightwards arrow on top space equals space 9 and stack A subscript y with rightwards arrow on top space equals space 16

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5
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Two forces, each of 10 N, act at a point P as shown in the diagram. The angle between the force vectors is 120° .

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What is the magnitude of the resultant force?

  • 5 space straight N

  • 10 space straight N

  • 17 space straight N

  • 20 space straight N

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1
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When no wind is present, a glider travels from the top of a peak in the west to the top of a peak of equal height in the east with constant speed V.

If a crosswind blows with speed W from north to south, which of the following expressions could represent the new direction of the glider?

  • theta subscript 0 space equals space sin to the power of negative 1 end exponent open parentheses V over W close parentheses

  • theta subscript 0 space equals space cos to the power of negative 1 end exponent open parentheses W over V close parentheses

  • theta subscript 0 space equals space tan to the power of negative 1 end exponent open parentheses W over V close parentheses

  • theta subscript 0 space equals space tan to the power of negative 1 end exponent open parentheses V over W close parentheses

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2
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A kayaker rows at k space equals space 5.0 space straight m divided by straight s from the north bank to the south bank of a river 200 space straight m wide, flowing east at r space equals 4.0 space straight m divided by straight s. The kayaker maintains a constant heading directly south.

Which of the following is the displacement the kayaker travels downstream between leaving the north and arriving at the south bank?

  • 100 space straight m

  • 160 space straight m

  • 200 space straight m

  • 250 space straight m

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3
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Two vectors A with rightwards arrow on top space equals space 12 space straight m divided by straight s at 45 degree above the horizontal and B with rightwards arrow on top space equals space 8.0 space straight m divided by straight s along the horizontal are combined to obtain a resultant vector R with rightwards arrow on top.

Which of the following is most nearly the ratio of the horizontal component of R with rightwards arrow on top to its vertical component?

  • 1.5

  • 1.9

  • 2.0

  • 2.5

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4
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A swimmer swims across a river from a point on the north bank to a point directly opposite on the south bank. To achieve this, the swimmer moves their starting position upstream. The river flows east with speed r and the speed of the swimmer relative to the water is k.

Which of the following expressions correctly describes the magnitude of the swimmer's resultant velocity v subscript R and their direction relative to the north bank of the river?

  • v subscript R space equals space square root of k squared space plus space r squared end root and tan space theta space equals space r over k

  • v subscript R space equals space square root of k squared space minus space r squared end root and sin space theta space equals space r over k

  • v subscript R space equals space k space plus space r and tan space theta space equals space r over k

  • v subscript R space equals space square root of k squared space minus space r squared end root and cos space theta space equals space r over k

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5
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A hiker starts at a point and travels d subscript 1 space equals space 5.0 space km north, then d subscript 2 space equals space 3.0 space km east, and finally d subscript 3 space equals space 4.0 space km southwest at an angle of 45 degree.

Which of the following is most nearly the magnitude of the hiker's displacement?

  • 5.8 space km

  • 6.5 space km

  • 7.0 space km

  • 7.8 space km

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