January 30, 2013
A ball tossed vertically in the air from ground
level can be modeled by the function,
where p(t) is the position of the ball above the
ground (in feet) after t seconds in the air.
January 30, 2013
January 30, 2013
The velocity of the ball, v(t), at time t seconds can be found by
taking the derivative of p(t). The velocity is the rate of change
of the position of the object.
The units of a velocity function is typically the units of the
position function per some unit of time. If the units of the
position function is feet, the units of the velocity in which the
object is moving might be feet/second.
Velocity also tells us the object's direction.
Find v(t) and state its units.
Recall from your physics days!!!
January 30, 2013
January 30, 2013
Is v(t) increasing,
decreasing, or constant?
How is the velocity graph
related to the position
graph?
January 30, 2013
Does a negative velocity mean the ball is
"slowing down"?
Answer: No. As v(t) is getting further away
from the x-axis in either direction, the ball's
velocity is increasing.
object has no
velocity at this
point
January 30, 2013
At what time
does the ball have the greatest velocity? Rank in order from
smallest to greatest.
January 30, 2013