VIEWS: 40 PAGES: 2 POSTED ON: 1/30/2010
Accelerated motion problems 1) A rock falls from rest, with constant acceleration 10 m/s2. The acceleration is constant, i.e. air friction is negligible in this case. (a) What will be its velocity after 3 s of fall? and (b) How far will it fall in 3 s? A. arithmetic method a) a = 10 m/s/s means that the rock gains velocity by _________ (______) in each second. (number) (units) in 3 s of fall, it gains in velocity ______ m/s since it starts from rest, its final velocity is ______ m/s b) The velocity grows from ______ m/s at t=0 to the average velocity is .5*(______+______) or distance travelled, with this average velocity, in 3s is vavet or ______ m/s * _____ s = ________ (_____) B. algebraic method a) The acceleration, a= 10 m/s/s, time t=3s, and vo=0 m/s. Substituting into v = vo + at yields the final velocity v = ______ + _____ * ______ = _____ (______) b) Substituting into x = vot + .5at2 yields ______ * ______ + 0.5 * ______ * (______)^2 = ______ (______) ______ m/s ______ m/s 2) A ball is thrown downward, and released with velocity 20 m/s, to fall freely from the instant the clock is started (again friction is negligible). (a) What will be its velocity after 3 s? and (b) How far will it fall in 3 s? A. arithmetic method a) a = 10 m/s/s means that the rock gains velocity by ___________ (______) in each second. in 3 s of fall, it gains in velocity ______ m/s since it starts from 20 m/s, its final velocity is ______ m/s b) The velocity grows from ______ m/s at t=0 to ______ m/s at t=3s. the average velocity is .5*(______ + ______) or distance traveled, with this average velocity, in 3s is vavet or ______ m/s * ______ s = ________ (______) B. algebraic method a) The acceleration, a=10 m/s/s, time t=3s, and vo=20 m/s. Substituting into v = vo + at yields the final velocity v = ______ + ______ * ______ = ______ (__m/s____) b) Substituting into x = vot + .5at2 yields ______ * ______ + 0.5 * ______ * (______)^2 = ______ (______) ______ m/s 3) A ball is thrown upward, and released with velocity 8 m/s, to fall freely from the instant the clock is started (again friction is negligible). (a) What will be its velocity after 3 s? and (b) Where will it be in 3 s? A. arithmetic method (Define downward to be the positive direction). a) a = 10 m/s/s means that the rock gains velocity by ___________ (______) in each second. in 3 s of fall, it gains in velocity ______ m/s since it starts at -8 m/s, its final velocity is ______ m/s b) The velocity grows from ______ m/s at t=0 to ______ m/s at t=3s. the average velocity is .5*(______ + ______) or distance travelled, with this average velocity, in 3s is vavet or ______ m/s * ______ s = ________ (______) B. algebraic method a) The acceleration, a=10 m/s/s, time t=3s, and vo= -8 m/s. Substituting into v = vo + at yields the final velocity v = ______ + ______ * ______ = ______ (______) b) Substituting into x = vot + .5at2 yields ______ * ______ + 0.5 * ______ * (______)^2 = ______ (______) ______ m/s 4) An arrow is shot at 30 m/s straight up at a bird perched 20 m above the ground. How long does the bird have to live after the arrow is fired? Let’s decide to make up positive this time, then: vo = __________ (_________) and a = __________ (_________) and then plug into x = vot + .5at2 to solve for time t. You will have to use the quadratic equation which will give you two solutions for t. What do BOTH solutions mean?