Kinematics in Two or Three Dimensions

Vectors and Scalars

Vector

Scalar

has magnitude and direction

Eg: Displacement, velocity,force

magnitude only

Eg: Mass,Time, Temperature

Addition of vectors

one dimension

simple addition and subtraction

two dimension

Right angle

Not at right angle

Pythagorean Theorem

tail-to-tip method

Subtraction of Vectors and Multiplication of Vector by scalar

Negative of vector has same magnitude but different direction

Adding Vectors by Components

Vector is multiplied by a scalar c. cV has the same direction

Perpendicular components found using trigonometric function

Adding vectors by components

One-dimensional components
-added arithmetically

Unit Vectors

unit-vector

Vector Kinematics

Vector kinematics new

Projectile Motion

Horizontal

Vertical

-Acceleration is zero
-Velocity remains constant at any point

Acceleration(downwards)= image

Relative velocity

Relative velocity new

Scalar product : a · b = |a| × |b| × cos(θ)

Vector product : |AxB| = A B sinθ.

Vbs =Vbw + Vws
Vbs is boat'svelocity
Vbw is boat's velocity(in water frame)
Vws is water's velocity(in shore frame)

Direction(angle)find using trigonometric function

Pythagorean theorem used to find the velocity

Low Jing Ning A20SC0126