CALCULUS
Higher Concepts of Mathematics
3.
Give the physical interpretation of the following equation relating
the force, F, applied to an object, its mass m, its instantaneous
velocity v and time t.
F
mdv
dt
This equation includes the derivative dv/dt; the derivative of the
velocity with respect to time. It is the rate of change of velocity
with respect to time. The force applied to an object equals the
mass of the object multiplied by the rate of change of velocity with
respect to time.
4.
Give the physical interpretation of the following equation relating
the acceleration a, the velocity v, and the time t.
a
dv
dt
This equation includes the derivative dv/dt; the derivative of the
velocity with respect to time. It is a rate of change. The
acceleration equals the rate of change of velocity with respect to
time.
Graphical Understanding of Derivatives
A function expresses a relationship between two or more variables. For example, the distance
traveled by a moving body is a function of the body’s velocity and the elapsed time. When a
functional relationship is presented in graphical form, an important understanding of the meaning
of derivatives can be developed.
Figure 4 is a graph of the distance traveled by an object as a function of the elapsed time. The
functional relationship shown is given by the following equation:
s = 40t
(5-4)
The instantaneous velocity v, which is the velocity at a given instant of time, equals the
derivative of the distance traveled with respect to time, ds/dt. It is the rate of change of s with
respect to t.
MA-05
Page 34
Rev. 0
