Distance, Speed Notes

Distance, Speed  There are 4 ways to quantify motion:  How far (distance/displacement)  How fast (speed/velocity)  Direction  Acceleration

Distance  Distance of motion is the measured movement of one object relative to another. The object we compare to is called the reference object, and is usually the Earth  We should consider the reference object stationary. When an object moves relative to another object, it will have traveled some distance

Distance  Distance is a scalar quantity (magnitude only, no direction)

Displacement  Displacement is the change in position of an object, or the length of a straight line from its initial position to its final position. When an object moves relative to another, it will not necessarily have undergone any displacement.

Displacement  Displacement is a vector quantity (magnitude and direction are described)  Δx = x f - x i

Speed  Speed is described as the rate of movement Average speed = distance / time Example: A race car goes around a 1 mile oval track in 15 seconds. Its average speed would be 240 mi/hr

Speed  Speed is a scalar quantity Traditional Units:  Metric units: m/s  English units: mi/hr, ft/s

Velocity  Velocity is described as the rate of displacement Average velocity = displacement / time Example: A race car goes around a 1 mile oval track in 15 seconds. Its average velocity would be 0 mi/hr.

Velocity  Velocity is a vector quantity. It has the same units as speed, but direction should be signified.

Velocity  If a graph is drawn with displacement on the y-axis and time on the x-axis, the slope of that graph would show the average velocity Slope = rise/run = Δy / Δx = Δx / Δt = Δd / Δt = v ave

Velocity  Therefore, a steep positive slope corresponds to a large average velocity, a steep negative slope would correspond to a large negative average velocity, a flatter positive slope would correspond to a smaller positive average velocity, etc.

Velocity v ave = Δx / Δt = Δd / Δt = (x f – x i ) / (t f – t i ) Instantaneous Velocity: Velocity at a given instant in time. This cannot be calculated without knowing the constant acceleration or using calculus.