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Physics - Vectors and Simple Motion

Remember the difference between vector and scalar quantities. Quantities that do not have directional components are called scalar quantities. Quantities that do have directional components are called vector quantities.

Speed is a scalar quantity. Twenty meters per second describes speed.

Velocity is a vector quantity. Twenty meters per second in a westward direction describes velocity.

Distance is a scalar quantity. Three-hundred miles describes distance.

Displacement is a vector quantity. Three-hundred miles in a westward direction describes displacement.

In order to calculate the sum of two vectors:
  1. Maintain each vector in its original orientation.
  2. Place tail of one vector to head of the other vector.

You will need to remember the following trigonometric functions of a right triangle. Sine equals opposite over hypotenuse. Cosine equals adjacent over hypotenuse. Tangent equals opposite over adjacent.

The relationship between speed and distance: Speed is measured in units of distance per time. It can be measured in meters per second, inches per hour, miles per hour, miles per day, or any other quantity that represents distance over time. If we are told that a car has traveled 200 miles in 4 hours, we might conclude that its speed for the whole trip was 200 miles per 4 hours which equals 50 miles per hour. Total distance and total time do not reveal instantaneous speed for any moment during its trip. They reveal average speed.

Rule number 1:
Average speed equals total distance divided by total time, the relationship between velocity and displacement. Because displacement and velocity are both vector quantities, they can be related in the same way that speed and distance are related.

Rule number 2:
Average velocity equals displacement divided by time or v = x/t, where displacement equals x, elapsed time equals t, and velocity equals v. A bar above a letter is used to designate that it is an average.

Thus, average velocity is symbolized by a v with a bar over it. A change in velocity over a particular period of time is called acceleration. If at one moment an object is traveling at 40 meters per second and 5 seconds later it is traveling at 50 meters per second, the object has changed its velocity. It has, therefore, accelerated. It has increased its velocity by 10 meters per second which we obtained by subtracting 40 meters per second from 50 meters per second and it has achieved this increase in 5 seconds. We do not know if the car picked up speed at a constant rate. So we do not know the car’s instantaneous acceleration. But we do know that on average, it picked up speed by 10 meters per second in 5 seconds. Its average acceleration, therefore, is 10 meters per second in 5 seconds which is the same as saying 2 meters per second per second. This is represented by writing 2 m/sec2.

Rule number 3:
Average acceleration equals change in velocity divided by change in time or

A= (Vfinal – Vinitial) / (Tfinal – Tinitial).

Uniformly accelerated motion along a straight line: If a moving body is accelerating at a constant rate along a straight line, its velocity is constantly changing but it is changing at a constant rate.

Rule number 4:

  1. For a body in uniformly accelerated motion, final velocity equals initial velocity plus acceleration times time or V = Vinitial + AT.
  2. For a body in uniformly accelerated motion, displacement equals initial velocity times time plus one-half acceleration times time squared, or X = VinitialT + ½ AT2.

The earth’s gravity produces uniform accelerated motion along a straight line. For freely falling bodies, the earth’s gravity produces uniform acceleration along a straight line. The uniform acceleration produced by earth’s gravity is known as G and G equals 9.8 m/sec2. For ease of calculation, assume G equals 10 m/sec2. Acceleration, depending on its direction may increase or decrease velocity. If an object’s velocity is increasing, then the object is accelerating in the same direction as its velocity. If on the other hand the object’s velocity is decreasing, the object is still accelerating but the acceleration is in the direction opposite to the velocity. Acceleration that decreases velocity is often described as negative acceleration or deceleration.