Accelerated motion problems (printer-friendly version)

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 ______ m/s

\ the average velocity is .5*(_____+______) or ______ m/s

\ distance travelled, with this average velocity,

in 3s is v_ave×t or ______ m/s * _____ s = ________ (_____)

B. algebraic method

a) The acceleration, a= 10 m/s/s, time t=3s, and v_o=0 m/s.

Substituting into v = v_o + a×t yields the final velocity

v = ______ + _____ * ______ = _____ (______)

b) Substituting into Dx = v_o×t + .5×a×t² yields

______ * ______ + 0.5 * _____ * (_____)^2 = _____ (______)

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 ______ m/s

\ distance traveled, with this average velocity,

in 3s is v_ave×t or ______ m/s * ______ s = ________ (_____)

B. algebraic method

a) The acceleration, a=10 m/s/s, time t=3s, and v_o=20 m/s.

Substituting into v = v_o + a×t yields the final velocity

v = ______ + ______ * ______ = _____ (______)

b) Substituting into Dx = v_o×t + .5×a×t² yields

______ * ______ + 0.5 * _____ * (_____)^2 = ______ (______)

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 ______ m/s

\ distance travelled, with this average velocity,

in 3s is v_ave×t or ______ m/s * ______ s = ________ (_____)

B. algebraic method

a) The acceleration, a=10 m/s/s, time t=3s, and v_o= -8 m/s.

Substituting into v = v_o + a×t yields the final velocity

v = ______ + ______ * ______ = ______ (______)

b) Substituting into Dx = v_o×t + .5×a×t² yields

______ * _____ + 0.5 * ______ * (______)^2 = ______ (______)

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:

v_{o =} __________ (_________) and a = __________ (_________)

and then plug into Dx = v_o×t + .5×a×t² 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?

Solutions are: .764 and 5.24 seconds.