Dear MD7
I am not sure that I understand this but you might...
[copied from
]
The derivative measures rates of change for functions that are continuous and variable. Functions like this are used extensively in science.
If there is a relationship between distance travelled (s) and time (t), then the derivative of distance with respect to time, ds/dt, gives the velocity (v) at any time.
Example: A particle moves so that its distance (in m) from a fixed point is given by
s = 2t2 - 3t + 1, where t is time in seconds. Find its velocity after 4s.
The velocity, v, is given by ds/dt so we differentiate the above equation with respect to t:
v = ds/dt = 4t - 3. When t = 4s, v = 13m/s.
If there is a relationship between the velocity of a particle (v) and time (t), then the derivative of v with respect to t, dv/dt, gives the acceleration (a) at any time.
Example: The above particle's velocity is given by v = 4t - 3. What it is acceleration after 1s.
The acceleration, a, is given by dv/dt so we differentiate the above equation with respect to t:
a = dv/dt = 4. The acceleration is constant at 4m/s2.
If there is a relationship between Energy (E) and time (t), then the derivative of E with respect to t, dE/dt, gives the power (P) at any time.
Example: A device uses up energy in a manner dependent on time: E = t3, where E is energy in Joules and t is the time in seconds. Find the power being used after 2s.
The power, P, is given by dE/dt so we differentiate the above equation with respect to t:
P = dE/dt = 3t2. The power after 2s is therefore 12W.
[© 2001 Kryss Katsiavriades]
Good luck!!
Adam B-Browne