3.1-3.3
3.1 Position, Displacement, and Average Velocity
Position is where an object is at any particular time. It is usually denoted by the variable x.
Frame of reference: set of axes from which the position and motion of an object are described
Displacement is the change in position. It is a vector and indicates direction. It can be positive or negative. the magnitude is always postive.
Δx=xf−x0,
where Δx is displacement, xf is the final position, and x0 is the initial position.
Total displacement is the sum of individuall displacements
ΔxTotal=∑Δxi,
where Δxi are the individual displacements.
Distance traveled is the sum of the magnitudes and individual displacements.
Average velocity is the total displaceent divided by the time taken to travel between them (elapsed time). it can be negative.
3.2 Instantaneous Velocity and Speed
Instantaneous Velocity: how fast an object is moving anywhere along its path. it is the average velocity between two points on the path in the limit that the time between two events approaches zero.
the zeroes of the velocity function give the minimum and maximum of the position function.
v(t)=limΔt→0x(t+Δt)−x(t)Δt=dx(t)dt.
The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t:
v(t)=ddtx(t).
Average Speed: total distance traveled divided by elapsed time. Speed is a scalar.
Instantaneous speed: Instantaneous speed=|v(t)|.
Instantaneous velocity: we must specify the explicit for of the position function using the power rule.
3.3 Average and Instantaneous Acceleration
Average accelertaion is the rate at which velocity changes
m/s²
acceleration occurs when velocity changes in magnitude or direction, or both
Instantaneous Acceleration: acceleration at a specific instant in time. it is the derivative of the veocity function.
a–=ΔvΔt=vf−v0tf−t0,