(a)
To calculate: The position
(a)
Answer to Problem 51RE
The required position vector is
Explanation of Solution
Given information:
The curve:
The x -component of acceleration = 2
At time t = 0 the position of the particle =
At time t = 0 the velocity of the particle =
Calculation:
The given curve along which the particle is moving is
The x -component of acceleration is 2.
So, for
The velocity of the particle is
And, the position of the particle is
It is known that the first derivative of the velocity vector
Now,
The velocity component of the particle at
Substitute 0 for
Substitute 0 for C in the expression
Thus, the velocity component of the particle is
It is known that the first derivative of the position vector
The position of the particle at t = 0 is
Substitute 0 for t and
Substitute
Also,
Hence, the required position vector is
(b)
To calculate: The speed of the particle when it is at the point
(b)
Answer to Problem 51RE
The required of the particle is 2.324.
Explanation of Solution
Given information:
The curve:
The x -component of acceleration = 2
At time t = 0 the position of the particle =
At time t = 0 the velocity of the particle =
Calculation:
The given curve along which the particle is moving is
The x -component of acceleration is 2.
So, for
The velocity of the particle is
And, the position of the particle is
It is known that the first derivative of the position vector
So,
At the point
Also, it is known that the magnitude of the velocity vector is the speed of the particle and the magnitude of a vector
Thus, the magnitude of the velocity vector at
Hence, the required of the particle is 2.324.
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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