University:
Felician University
Course:
PHYS-355 | Advanced Topics in Physics
Academic year:

2020
Views:

161

Pages:

1
Author:

5CelestialChronicle

Particle Motion Reference Guide Typically, if а particle is moving along the x-axis at any time, 1, x(t) represents the position of the particle; along the y-axis, y(I) is often used; along another straight line, s(I) is often used. In addition, v(I) is typically used to represent the velocity ofthe particle. In these types of particle motion proЬ!ems, • Position: x(I) or s(t) Velocity: v(t) = s'(t) Acceleration: a(t) = v'(t) = s"(I) • • • • "Initially" fueans when time 1 = О. "At the origin" means x(I) = О. "At rest" means velocity v(I) = О. Лs = s(I,)- s(t1) when the position functioп is given; ЛI 1,-11 1 Average velocity ofthe particle is v(I) dl when the velocity function is given. Average velocity of the particle is -f" t2 -t1 • о Average acceleration ofthe particle is ti дv = v(t,) -v(t,) Лt t2 -t1 1 -f" a(1)d1 when the acceleration given; Average acceleration ofthe particle is - t2 - t1 • • • • • • • • when the velocity fuпction is t1 fuпction is given. If the velocity ofthe particle is positive, then the particle is moving to the right ( or up). Ifthe velocity ofthe particle is пegative, then the particle is moving to the left (or down). Ifthe acceleration of the particle is positive, then the velocity is increasing. If the acceleration ofthe particle is negative, then the velocity is decreasing. Speed is the absolute value of velocity. Ifthe velocity and acceleration have the same sign (both positive or both negative), then speed is increasing. Ifthe velocity and acceleration are opposite in sign (one is positive and the other is negative), then speed is decreasing. То determine total distance traveled over а time interval, you must calculate the sum of the,absolute values ofthe differeпces in positioп between all resting points or calculate J,'' iv(t)I dl. Displacement can Ье determined using displacemenl = f,, v(I) dl ,, the area under the absolute value of the velocity curve, • 1 J',,' v(t) dt • То determine the final position of а particle use s(t2 ) = s (t1 ) + • Todetenµinethefinalvelocityofaparticleuse v(12 )=v(11 )+J''a(t) dt ,, r