A stone is dropped from a tall building t=0 and strikes the ground. Illustrate a graph that best shows the velocity of the stone after it is dropped.

Question

Please create a graph that would best describe the velocity of the following problem or situation.

Answer 1

See my illustration at https://openprocessing.org/sketch/749569

Answer 2

height of the stone = h(t) =-16t^2 + vot + ho

the t^2 term represents the effect of gravity's acceleration

where t = time in seconds

h= height in feet

vo = initial velocity, which in this case looks like 0

ho = initial height or the height of the tall building

h(t) = -16t^2 + ho

velocity = the derivative of h(t) or h'(t)

v(t) = -32t

the graph of h(t) is a downward opening parabola

the graph of v(t) is a fairly steep downward sloping straight line through the origin (0,0) with slope = -32

or if measured in meters, with the metric system

4.9 meters = 16 feet, approximately

h(t) = -4.9t^2 + ho

and

v(t) = h'(t) =-9.8t which has a similar graph, just not quite as steep.

But if the stone is dropped with some initial velocity

then v(t) = -32t +vo

or

v(t) =-9.8t + vo

where vo is how fast the stone is thrown when dropped

the graph is still the same basic straight line, just shifted vertically by vo units, leaving it parallel to the graph with vo=0

velocity, v(t), is measured on the vertical or y axis, with time, t, measured on the horizontal or x axis.

the negative velocity means the stone is going down