(a)
The velocity of the particle.
(a)
Explanation of Solution
Given:
The position of the particle at
The position of the particle at
The velocity of the particle is
Formula used:
Write the expression for the average velocity.
Here,
Here,
Write the expression for the average velocity of the particle.
Here,
Solve the above equation for
Calculation:
Substitute
Substitute
Conclusion:
Thus, the initial velocity is
(b)
The acceleration of the particle.
(b)
Explanation of Solution
Given:
The position of the particle at
The position of the particle at is
The velocity of the particle is
Formula used:
Write the expression for the acceleration of the particle.
Here,
is the change in the velocity vector and is the change in time.
Here,
Calculation:
Substitute
Conclusion:
The acceleration of the particle is
(c)
The velocity of the particle as the function of time.
(c)
Explanation of Solution
Given:
The position of the particle at is.
The position of the particle at is
The velocity of the particle is
Formula used:
Write the expression for the velocity of the particle as the function of time.
Here,
Calculation:
Substitute
Conclusion:
Thus, the velocity of the particle as the function of timeis
(d)
The position vector of the particle as the function of time.
(d)
Explanation of Solution
Given:
The position of the particle at is.
The position of the particle at is
The velocity of the particle is
Formula used:
Write the expression for the position vector as the function of time.
Calculation:
Substitute
Conclusion:
The position vector of the particle as the function of time is:
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