All: learn the meanings of average and difference and final.
Learn how to take a definition and turn it into an equation for a quantity used in the definition
5) While vavg = (vf+vi)/2 when ( and only when) a is constant, this is not a definition of vavg. Definition of vavg in x direction is deltax/delta t same applies in any other direction
8) a DOES NOT = vavg/delta t. It is remarkable that this is still an issue. a = change in v divided by time it took change to occur or a = (vf-vi)/delta t = delta v/delta t AND delta v DOES NOT = vavg. By the way, the relation for a in the previous sentence is a definition not just an equation.
12) delta x = vavg delta t It is amazing how many of you correctly identified vavg as 15 m/s and the said delta x = 30 m/s x delta t anyway. vavg does not = vf or = vi unless a is zero. If a is constant vavg = (vf+vi)/2 as noted above (and about a hundred other times)
17) Vectors and Scalars:
Position is a vector. You have to give direction and distance, i.e. what direction and how far you are from the origin. 5 miles doesn't give your position. 5 miles at 15 degrees north of east from Brush's deli ( a sort of origin around here) does give your position. 5 miles is called the magnitude of this position vector. 15 deg N of E is the direction, obviously.
Displacement is the change in position so naturally it is a vector (position f - position i). In other words, its not enough to say I moved 2 miles, that's just the magnitude of the displacement, you also need to say what direction.
Since velocity is the rate of displacement, i.e. rate of change of position, it too is a vector. It has a magnitude and a direction. Speed is just the magnitude of velocity and does not have a direction so its a scalar. Average speed is distance traveled over time and is non zero even when going in a complete circle. Average velocity going around a complete circle is zero since position f = position i and displacement is zero. At any one instant someone going in a circle has an instantaneous velocity, but the average is zero for a complete circle.
acceleration is the rate of change of velocity and has direction so it is a vector.
Energy is not a vector, it has no direction. You may be confused because one can calculate KE from velocity components. KE equals m vsquared/2. If one has orthogonal (i.e. at right angle) components such as x and y, then the v squared = vx squared + vy squared and
KE = m vx squared/2 + m vy squared/2 but that doesn't mean energy has x and y components, its just how Pythagoras works out. The energy is just there; it has no direction. KE depends only on total speed.
13) A - sign in front of a vector doesn't mean its making things smaller, it means the vector is pointed in the negative direction. Negative acceleration usually means accelerating down or left or south or west by convention. The acceleration due to gravity in free fall is always down or negative. It doesn't matter whether the ball is going up and slowing down, or stopped for an instant, or going down and speeding up, the acceleration is down and therefore negative.
Energy is not a vector, it has no direction. You may be confused because one can calculate KE from velocity components. KE equals m vsquared/2. If one has orthogonal (i.e. at right angle) components such as x and y, then the v squared = vx squared + vy squared and
KE = m vx squared/2 + m vy squared/2 but that doesn't mean energy has x and y components, its just how Pythagoras works out. The energy is just there; it has no direction. KE depends only on total speed.
13) A - sign in front of a vector doesn't mean its making things smaller, it means the vector is pointed in the negative direction. Negative acceleration usually means accelerating down or left or south or west by convention. The acceleration due to gravity in free fall is always down or negative. It doesn't matter whether the ball is going up and slowing down, or stopped for an instant, or going down and speeding up, the acceleration is down and therefore negative.
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