Question

An object is dropped from rest. Ignore air-resistance.

         (a) Predict what the graph of its y-position as a function of time looks like

         (b) Predict what the graph of its y-velocity as a function of time looks like.

. What would happen if you used a coffee filter instead of a ball? Make a prediction of what a y-velocity versus time graph might look like.

Answer 1

for an object dropped

v_o = initial velocity

a = acceleration = - g

t = time of travel

v(t) = final velocity at any time "t"

y(t) = position at any time "t"

y_o = initial position

a)

position at any time "t" is given as

y(t) = y_o + v_o t + (0.5) a t²

y(t) = y_o + (0) t + (0.5) (-g) t²

y(t) = y_o - (0.5) (g) t²

b)

velocity at any time "t" is given as

v(t) = v_o + a t

v(t) = 0 + (-g) t

v(t) = - gt

Since there is no air-resistance, coffee filter and ball will follow the same path. hence the y-velocity and time graph for both of them will be similar.