324 Basic Engineering Mathematics
Now try the following Practice Exercise
Practice Exercise 138 Rates of change
(answers on page 355)
1. An alternating current, i amperes, is given by
i = 10 sin 2πft, where f is the frequency in
hertz and t is the time in seconds. Determine
the rate of change of current when t = 12 ms,
given that f = 50 Hz.
2. The luminous intensity, I candelas, of a lamp
is given by I = 8 × 10 −4 V 2 , where V is the
voltage. Find
(a) the rate of change of luminous intensity
with voltage when V = 100 volts.
(b) the voltage at which the light is increasing at a rate of 0.5 candelas per volt.
3. The voltage across the plates of a capacitor at
any time t seconds is given by v = V e −t /CR ,
where V , C and R are constants. Given
V = 200 V, C = 0.10 μF and R = 2 M, find
(a) the initial rate of change of voltage.
(b) the rate of change of voltage after 0.2 s
4. The pressure p of the atmosphere at height h
above ground level is given by p = p 0 e −h/c ,
where p 0 is the pressure at ground level and c
is a constant. Determine the rate of change of
pressure with height when p 0 = 1.013 × 10 5
pascals and c = 6.05 × 10 4 at 1450 metres.