Iinstantaneous velocity can be obtained from a position­time curve of a
moving object.
LEARNING OBJECTIVE [ edit ]
Recognize that the slope of a tangent line to a curve gives the instantaneous velocity at that point
in time
KEY POINTS [ edit ]
Velocity is defined as rate of change of displacement.
The velocity v of the object can be computed as the derivative of position: .
The equation for an object's position can be obtained by evaluating the integral of the equation
for its velocity from time t0 to a later time tn.
TERMS [ edit ]
integral
also sometimes called antiderivative; the limit of the sums computed in a process in which the
domain of a function is divided into small subsets and a possibly nominal value of the function on
each subset is multiplied by the measure of that subset, all these products then being summed
velocity
a vector quantity that denotes the rate of change of position with respect to time, or a speed with
the directional component
tangent
a straight line touching a curve at a single point without crossing it there
Give us feedback on this content: FULL TEXT [ edit ]
Calculus has widely used in physics and engineering. In this atom, we will learn that
instantaneousvelocity can be obtained
from a position­time curve of a moving
object by calculating derivatives of the
curve.
Velocity is defined as rate of change
of displacement. Theaverage velocity of
an object moving through a displacement
(
) during a time interval (
described by the formula: ) is
.
What will happen when we reduce the
time interval Register for FREE to stop seeing ads
and let it approach 0? The average velocity becomes instantaneous velocity
at time t. Suppose an object is at positions x(t) at time t and at time . The
velocity v of the object can be computed as the derivative of position: . Instantaneous velocity is always tangential
to trajectory. Slope of tangent of position or displacement time graph is instantaneous
velocity and its slope of chord is average velocity.
Instantaneous Velocity
The green line shows the tangential line of the position­time curve at a particular time. Its slope is the
velocity at that point.
On the other hand, the equation for an object's position can be obtained mathematically by
evaluating the definiteintegral of the equation for its velocity beginning from some initial
period time t0 to some point in time later tn. That isx(t) = x_0 + \int_{t_0}^{t} v(t')~dt',
where x0 is the position of the object at t=t0. For the simple case of constant velocity, the
equation gives $x(t)­x_0 = v_0 (t­t_0)$.