Concept explainers
a.
To find: The initial position of the particle.
a.
Answer to Problem 4QQ
The initial position of the particle is
Explanation of Solution
Given information: The position of particle is
Calculation: The position of particle is
For initial position put
Therefore the initial position of the particle is
b.
Find the initial velocity of the particle at time
b.
Answer to Problem 4QQ
Initial velocity is
Explanation of Solution
Given information: The position of particle is
Calculation: The position of particle is
To find initial velocity we find the first derivative.
Thus, initial velocity is
c.
When the particle is moving to right.
c.
Answer to Problem 4QQ
When the particle is moving to right then
Explanation of Solution
Given information: Initial velocity is
Calculation: Initial velocity is
Particle is moving to the right so velocity is positive.
Time is lie between
When the particle is moving to right then
Draw the graph of this equation:
d.
Find the acceleration of the particle at any time
d.
Answer to Problem 4QQ
Acceleration is
Explanation of Solution
Given information: Velocity is
Calculation: Velocity is
Acceleration is derivative of velocity.
Therefore acceleration is
e.
Find the speed of the particle at the moment when
e.
Answer to Problem 4QQ
The speed of the particle at the moment when
Explanation of Solution
Given information: The position of particle is
Calculation: The position of particle is
Factorize the equation we get:
Time cannot be negative.so
Speed is absolute value of velocity.
Therefore speed is
Put
Therefore speed is
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
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