function application in calculus?

Question

The Heaviside function H is defined below. It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. The Heaviside function can also be used to define the ramp function y = ctH(t), which represents a gradual increase in voltage or current in a circuit.

http://www.webassign.net/www30/symImages/e/b/7b468910ea394002f905894a548898.gif

as seen in above link, H(t)={ 0 if t<0, 1 if t> or = 0

(a) Write a formula for V(t) in terms of H(t) if the switch is turned on at time t = 0 and the voltage is gradually increased to 140 volts over a 70 second time interval.

(b) Write a formula for V(t) in terms of H(t) if the switch is turned on at time t = 6 seconds and the voltage is gradually increased to 220 volts over a period of 55 seconds.

Answer 1

H(t) = 0 if t < 0, H(t) = 1 if t >= 0;
♣ c=140/70 = 2 V/s; thus for t > 0
V(t) = 2t*(1 -H(t -70)) +140*H(t -70);
♦ c=220/55 = 4 V/s; thus for -∞ < t < +∞
V(t) = 4(t-6)*(1 -H(t -6-55))*H(t-6) +220*H(t -6-55);
Check it; I think it works; click me if w/e;