# CH.1 - Displacement, Velocity, & Vectors

## 13 terms · Schaums' ch. 1

### Scalar Quantity

A quantity WITHOUT a direction; length, time, temp, mass and density are included

### Distance

we use 'l' to denote distance. It is a scalar quantity

### Average Speed

Scalar quantity; how fast something travels in space
avg. spd = total distance traveled / time elapsed

* on a distance vs. time graph, the slope of the line drawn is the avg spd. during a particular interval
** distance traveled is always positive and never decreases, thus the graph is always pos and never decreases

### Instantaneous Speed

limiting value of avg. spd.
change in distance over time, as the change in time approaches zero
** slope of the line tangent to the dis. vs. time graph

### Vector Quantity

physical concept that requires both direction and magnitude
ie: displacement, velocity, acceleration, force, etc
*written as a bold type or with an arrow overtop

### Displacement

a vector quantity
depicts distance from one point to another -> shortest distance avail.
gives direction as well
*often represented as 's' (with arrow on top to indicate it is a vector)

### Velocity

a vector quantity that embraces both spd and direction of motion

Avg. velocity = vector displacement / time taken

### Instantaneous Velocity

Avg velocity for a time interval that approaches zero
*slope of the tangent line of the velocity vs. time graph

### Tip to Tail Method

When adding vectors, place the tail of the 2nd vector at the tip of the first (and so on); you can add vectors in any order, and the resultant vector 'R' (w/ arrow on top) will still be correct

### Subtraction of Vectors

to subtract vectors, ie: subtract B from A, reverse the direction of B

A - B = A + (-B)

sin = opp/ hyp
cos = adj/ hyp
tan = opp/ adj

### Components of vectors

the direction with regards to the x or y axis of the 'R' vector
Note that:
Rx = Rcos(theta)
Ry = Rsin(theta)

R = the square root of (Rx^2) + (Ry^2)

** the ANGLE of R can be found by tan(theta) = Ry / Rx

### Unit Vectors

have a magnitude of 1 and are boldfaced and topped with a caret
unit vectors i,j, and k are assigned to the x,y,and z axes respectively
ex:
unit vector 3i = 3 unit vector in the +x direction
unit vector -5k = 5 unit vector in the -z direction

Note: R = Rxi + Ryj +Rzk