 # All quantities in Physics can be categorized as either a scalar or a vector quantity. A scalar quantity has magnitude (amount) only without direction.

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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 meters Displacement = 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 t ex: How fast is a car moving if it goes 30 meters in 5 seconds? v = Δ d/ Δ t v = 30 m / 5 s v = 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 = (v f + v i )/2 Or Ave v = Δ d/ Δ t Acceleration is the rate of change of velocity per unit of time. a = Δv/ Δ t What 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)/ 8s a = 2 m/s 2

You can calculate the distance traveled with a constant acceleration for the previous example using this formula; d = v i Δ t + ½ a Δ t 2 d = v i Δ t + ½ a Δ t 2 d = (0m/s)(8s) + ½ 2 m/s 2 (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. v f = v i + at v f = 0 m/s + (2 m/s 2 ) (8s) v f = 16 m/s note: the units (m/s 2 )(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 v f 2 = v i 2 + 2ad v f 2 = (0 m/s) 2 + 2(2m/s 2 )(64m) v f 2 = √256 m 2 /s 2 v f = 16 m/s

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