Chapter 2: Q5P (page 77)

In each of the following problems, z represents the displacement of a particle from the origin. Find (as functions of t) its speed and the magnitude of its acceleration, and describe the motion.
$z = z_{1} t + z_{2} (1 - t)$ Hint: See Problem 4; the straight line here is through the points $z_{1}$ and $z_{2}$

Short Answer

Expert verified

The part it follows is straight line.

Its speed is $z_{1} - z_{2}$ .

Acceleration $0$

$z_{i} = z_{2} and z_{f} = z_{2}$

Step by step solution

Given Information.

The given expression is $z = z_{1} t + z_{2} (1 - t)$ .

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form of $x + i y$ in which x is the real part and y is the imaginary part.

Simplify.

Rewrite the given equation.

$z (t) = z_{1} t - z_{2} t + z_{2} z (t) = [z_{1} - z_{2}] t + z_{2}$

It is of the form $z (t) = a t + b$

Therefore, it represents a straight line.

Find the velocity and acceleration.

Differentiate with respect to time.

$v (t) = \frac{d z (t)}{d t} v (t) = \frac{d}{d t} [(z_{1 -} z_{2}) t + z_{2}] v (t) = z_{1} - z_{2}$

Find the acceleration.

Differentiate the velocity with respect to time.

$\begin{array}{l} A (t) = \frac{d v (t)}{d t} \\ A (t) = 0 \end{array}$

Find the initial and final position.

Find $z (0)$ for the initial position.

$z (0) = z_{2}$

Find Final position.

$z_{f} = z_{1}$

Hence the path it follows is straight line.

Its speed is $z_{1} = z_{2}$ .

Acceleration 0

$z_{i} = z_{2} and z_{f} = z_{1}$

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Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Simplify.

Find the velocity and acceleration.

Find the initial and final position.

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In each of the following problems, z represents the displacement of a particle from the origin. Find (as functions of t) its speed and the magnitude of its acceleration, and describe the motion.z=z1t+z2(1-t)Hint: See Problem 4; the straight line here is through the points z1andz2

Short Answer

Step by step solution

Given Information.

Meaning of rectangular form.

Simplify.

Find the velocity and acceleration.

Find the initial and final position.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Magnetism

Circular Motion and Gravitation

Electromagnetism

Translational Dynamics

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.