Concept explainers
a.
Show that the velocity of an object slowed by air resistance satisfies the differential equation.
a.
Explanation of Solution
Given information: The resistance force on an object of mass m moving with velocity v is thus −kv for some positive constant k.
Proof:
Acceleration is the instantaneous rate of change of velocity so acceleration = dv/dt.
If m is the mass, then Force = mass x acceleration
It is also give that Force = -kv .
Therefore,
b.
To solve the differential equation to show that
b.
Explanation of Solution
Given information: The resistance force on an object of mass m moving with velocity v is thus −kv for some positive constant k.
Proof:
The required proved is obtained as,
c.
To find the one is slow to half its starting velocity in the shortest time.
c.
Answer to Problem 53E
A lighter mass will slow in time than a heavier mass.
Explanation of Solution
Given information: The resistance force on an object of mass m moving with velocity v is thus −kv for some positive constant k.
Calculation: The required solution is obtained as,
Substitute
Therefore as m increase, t increase if k remains constant. The lighter mass with then slow down faster.
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
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