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21 Mar 2020
The Heaviside function defined in Exercise 59 can also be used to define the ramp function 
, which represents a gradual increase in voltage or current in a circuit.
(a) Sketch the graph of the ramp function 
..
(b) Sketch the graph of the voltage 
in a circuit if the switch is turned on at time 
and the voltage is gradually increased to 120 volts over a 60-second time interval.
Write a formula for V(t) in terms of H(t) for 
(c) Sketch the graph of the voltage in a circuit if the switch is turned on at time 
seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds.
Write a formula for in terms of 
for 
.
The Heaviside function defined in Exercise 59 can also be used to define the ramp function , which represents a gradual increase in voltage or current in a circuit.
(a) Sketch the graph of the ramp function ..
(b) Sketch the graph of the voltage in a circuit if the switch is turned on at time and the voltage is gradually increased to 120 volts over a 60-second time interval.
Write a formula for V(t) in terms of H(t) for
(c) Sketch the graph of the voltage in a circuit if the switch is turned on at time seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds.
Write a formula for in terms of for .
Jarrod RobelLv2
27 May 2020
, where s is measured in centimeters and t in seconds. (Take thepositive direction to be downward)
. If a force
acts on the object, moving it along the x-axis from
to
, the Work-Energy Theorem states that the net work done is equal to the change in the kinetic energy: 
, where
is the velocity at
is the velocity at
be the position function of the object at time t and
,
the velocity and acceleration function. Prove the Work-Energy Theorem by first using substitution rule for Definite integrals (4.5.5) to show that
) and the substitution 
to evaluate the integral.
, the acceleration due to gravity, to find the mass, measured in slugs.)