Understanding Exponential Decay Models

Understanding Exponential Decay Models

Assessment

Interactive Video

Physics

11th - 12th Grade

Practice Problem

Hard

Created by

Emma Peterson

FREE Resource

The video tutorial begins with the introduction of a force equation, highlighting the role of mass as a constant factor. The teacher then explores acceleration as a function of velocity, discussing different forms of acceleration and their utility. The tutorial progresses to separating variables and integrating to express velocity as a function of position, v(x). The final section involves solving for v as a function of x, resulting in an exponential decay model, and interpreting the implications of this model in terms of drag and velocity.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial step taken to simplify the force equation?

Treating mass as a constant

Ignoring acceleration

Treating mass as a variable

Assuming velocity is constant

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which form of acceleration is chosen for efficiency in this problem?

d^2x/dt^2

d/dx of half v^2

v dv/dx

d/dt of v

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of separating variables in this context?

To simplify the equation

To eliminate velocity

To find acceleration

To prepare for integration

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What mathematical operation is performed after separating variables?

Differentiation

Subtraction

Multiplication

Integration

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the constant of integration determined?

By setting velocity to zero

Using initial conditions

By differentiating the equation

By assuming it is zero

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of model is derived from the integration process?

Linear growth model

Exponential decay model

Quadratic model

Logarithmic model

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the exponential decay model imply about the boat's velocity?

Velocity oscillates

Velocity decreases over time

Velocity increases over time

Velocity remains constant

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