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1.1Kinematics

Scalars and Vectors in One Dimension — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 2 of 14 1 quiz

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Lesson summary

1.1 Scalars and Vectors in One Dimension — AP PHYSICS 1 notes: Distinguish scalars from vectors and use signs and scalar operations to handle vectors in one dimension.Scalar — a quantity with magnitude only10 m s-1 is a scalar.Vector — a quantity with magnitude and direction10 m …

  • Vector arrows
  • Sign as direction
  • Axis convention
  • Equal and opposite
  • Multiply by a positive scalar
  • Multiply by −1

Section 1 of 9Scalar and vector quantities

Scalar
  • Scalar a quantity with magnitude only
  • 10 m s-1 is a scalar.
Vector
  • Vector a quantity with magnitude and direction
  • 10 m s-1 north is a vector.
Vector arrows
  • Vector arrows length is proportional to magnitude and the arrow points in the direction

Section 2 of 9Common pairs

ScalarVector
DistanceDisplacement
SpeedVelocity
MassWeight (force)

Section 3 of 9One-dimensional vectors

Sign as direction
  • Sign as direction positive and negative values show direction along one axis, so vector arrows are not needed
Axis convention
  • Axis convention whichever direction is positive must be used consistently
Equal and opposite
  • Equal and opposite vectors A and −A have equal magnitude and opposite direction

Section 4 of 9Scalar multiplication

1Multiply by a positive scalar
  • Multiply by a positive scalar magnitude changes, direction stays the same
    • (2B is twice as long)
2Multiply by −1
  • Multiply by −1 magnitude is unchanged and direction reverses

Section 5 of 9Adding and subtracting in one dimension

Addition
  • Addition add signed values: A + B
Subtraction
  • A − B = A + (−B), reversing B first
Resultant
  • Resultant the single vector with the same effect as the sum

Section 6 of 9Notation

Notation
Vector symbol
  • Vector symbol an arrow over the symbol, as on the College Board equation sheet
Magnitude
  • Magnitude written with vertical bars or without the arrow
Component equations
  • Component equations vx = vx0 + axt drops the arrows because the axis gives the direction

Section 7 of 9More from the specification

Initial velocity
  • Velocity at the start, u.
Parallelogram method
  • Vector addition using a parallelogram of vectors.
Initial speed
  • Speed at the start, u
Scalar multiplication
  • Multiplying a vector by a number.
Tip-to-tail method
  • Graphical vector addition where each vector starts at the tip of the previous one.
Fundamental
  • Lowest-frequency standing wave.

Section 8 of 9Key terms

TermMeaning
ScalarQuantity with magnitude only.
VectorQuantity with magnitude and direction.
ResultantVector sum of two or more vectors.
Scalar multiplicationMultiplying a vector by a number.

Section 9 of 9Exam technique

Avoid these mistakes
Treating a negative sign as a smaller quantity — it shows direction.
Using 10 m s-1 as a vector without a direction.
Forgetting to reverse a vector when subtracting.

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