Question:
An alternating current, 𝑖 amperes, is given by 𝑖 = 10sin2𝜋𝑓𝑡, where 𝑓 is the frequency in hertz and 𝑡 the time in seconds. Determine the rate of change of current when 𝑡 = 20𝑚𝑠, given that 𝑓 = 150𝐻𝑧.
Answer:
Firstly add the constant for frequency (𝑓 = 150Hz) into the equation given for current:
Differentiate and input the variable 𝑡, (remember 20ms = 0.02s).
Question:
The luminous intensity, 𝐼 candelas, of a lamp is given by:
where 𝑉 is the voltage. Find:
a) the rate of change of luminous intensity with voltage when 𝑉 = 200𝑣𝑜𝑙𝑡𝑠
b) the voltage at which the light is increasing at a rate of 0.3 candelas per volt.
Answer:
a)
b)
Question:
The voltage across the plates of a capacitor at any time 𝑡 seconds is given by
where 𝑉,𝐶 and 𝑅 are constants. Given 𝑉 = 300volts, 𝐶 = 0.12 × 10−6F and 𝑅 = 4 × 106Ω, find:
a) the initial rate of change of voltage
b) the rate of change of voltage after 0.5 s.
Answer:
a)
b)
Question:
The pressure 𝑝 of the atmosphere at height ℎ above ground level is given by:
where 𝑝0 is the pressure at ground level and 𝑐 is a constant. Determine the rate of change of pressure with height when 𝑝0 = 1.013 × 105 pascals and 𝑐 = 6.05 × 104 at 1450metres.
Answer:
a)
Input the 1450m height variable:
Question:
The volume, 𝑣 m3, of water in a reservoir varies with time 𝑡, in minutes. When a valve is opened the relationship between 𝑣 and 𝑡 is given by:
Calculate the rate of change of water volume at the time when 𝑡 = 3 minutes.
Answer:
