Question

equations .luentily ewery the .に0, a + variable in each of Velocity of a b。dg as a hnch 2. ot +tgta Csince initial v 2. AC 2 In the axes below sketch the position-time, velocity-time, and acceleration-time graphs for a) A ball falling from a height h without air resistance; b) a coffee filter falling from the same height h, but in a situation where air resistance is import. (use different color pencils for each situation and carefully label your sketches) time time ume

Answer 1

We know that x = ut + 0.5at^2 where x is the displacement

For a falling object, u=0. So, x = 0.5*a*t^2

a =constant for a falling object which is gravitational acceleration "g"

The graph for position vs time will be a parabola

We know that v = at

So the graph for velocity vs time is a straighline passing through origin with slope "g"

Acceleration throughout the journey is constant. So graph will be a horizontal line

For Part b)

When air resistance is not considered, all the graphs for coffee filter will also be the same

When air resistance is considered,

We can say that eventually after a long time acceleration becomes zero due to balancing of gravity and force of resistance

So the graph will be similar to an exponential decay

For velocity, graph will be of the form V(1-e^-kt) where V is the terminal velocity

So it starts similar to a straighline but soon deviates and becomes a horizontal line

For the position graph,

It starts like a parabola but soon becomes a straightline