All quantities in Physics can be categorized as either a scalar or a vector quantity.

A scalar quantity has magnitude (amount) only without direction. Ex. 4 meters, 3 seconds.

A vector quantity has magnitude with direction. Ex 4 meters North, 5 Newtons East.

note: the units for force are Newtons (N)

A vector is drawn as an arrow to indicate direction and a length proportional to the quantity.

Ex. 6 Meters East

The length of this arrow is 6 cm s the scale would be 1 m = 1 cm.

Distance is the length the object travels.Displacement is the length with direction from the

beginning of the journey to the end in a straight line.

Ex. A student walks 5 meters east and then 12 meters North

Distance = 17 metersDisplacement = 13 m @ 67° N of E (using

geometry.

The distance a body moves per unit of time is called speed. There is instantaneous speed , average speed,

and final speed.Velocity is a vector quantity of speed with direction.

v = Δ d/ Δ tex: How fast is a car moving if it goes 30 meters in 5

seconds?v = Δ d/ Δ t

v = 30 m / 5 sv = 6 m/s

Average velocity is the sum of the initial velocity and final velocity divided by 2. It is also the total distance

traveled divided by the total time elapsed.

Ave v = (vf + vi)/2Or

Ave v = Δ d/ Δ t

Acceleration is the rate of change of velocity per unit of time.

a = Δv/ Δ tWhat is the acceleration of a ball rolling from rest down a

hill to a speed of 16 m/s in 8 seconds?a = Δv/ Δ t

a = (16m/s – 0 m/s)/ 8sa = 2 m/s2

You can calculate the distance traveled with a constant acceleration for the previous example using this

formula; d = vi Δ t + ½ a Δ t2

d = vi Δ t + ½ a Δ t2

d = (0m/s)(8s) + ½ 2 m/s2 (8s)2

64 m

We can also calculate how fast the ball is going when it reaches the end of the hill if we were not given it.

vf = vi + at

vf = 0 m/s + (2 m/s2) (8s)

vf = 16 m/s

note: the units (m/s2)(s) gives you m/s

If you are given the time use this formula. If you are not given time but you have the distance use the next one.

or

vf2 = vi

2 + 2ad

vf2 = (0 m/s)2 + 2(2m/s2)(64m)

vf2 = √256 m2/s2

vf = 16 m/s