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Δt or t : change in time or time (s) Δv : change in velocity (m/s) v i: initial velocity (m/s) v f: final velocity (m/s) a : acceleration (m/s2) (note: on many different equation sheets x is substituted by d for displacement) Variables (mks unit) Δy or y : change in position or displacement (m) in the y axis Δv : change in velocity (m/s)
1. Constant acceleration in 1-D. Let x(t) represent the position of a particle at time t. Then x! is its velocity, v, and v!=a is its acceleration, which we assume is constant. This last equation is separable: dv=adt. Integrating we find v(t)!v(0)=at, or, using the notation 0v(0)=v, 0 v=v+at. This gives the differential equation for x: 0
In everyday conversation we usually talk about velocity in kilometres per hour (km/h), but need to use metres per second in physics formulas. You can convert km/h to m/s by dividing by 3.6 (this is an exact value and has an infinite number of sig digs). The answer from Example 5 would be 29.4m/s.
The formula v = r is true for a wheel spinning about a fixed axis, where v is speed of points on rim. A similar formulas v CM = r works for a wheel rolling on the ground. Two very different situations, different v’s: v = speed of rim vs. v cm = speed of axis. But v = r true for both.
Speed vs. Velocity. Speed is a scalar (how fast something is moving regardless of its direction). Ex: v = 20 mph. Speed is the magnitude of velocity. Velocity is a combination of speed and direction. Ex: v = 20 mph at 15° south of west.
In this chapter, we study speed, velocity, and acceleration for motion in one-dimension. One dimensional motion is motion along a straight line, like the motion of a glider on an airtrack.
Lecture 1: The meaning of vectors. Because we inhabit a world with more than one spatial dimension, physical phenomena frequently require us to distinguish between. Scalar : a quantity specified by a single number; Vector : a quantity specified by a number (magnitude) and a direction;
