Calculus I · Unit 3B · practice
Physics Application Studio
Practice Physics Application Studio with cumulative integral-calculus problems designed to test setup, computation, units, and interpretation.
Section overview
Physics and quantitative applicationsWhat this section is building
Practice Physics Application Studio with cumulative integral-calculus problems designed to test setup, computation, units, and interpretation.
Work adds force through distance, pumping adds slice weight through lift distance, pressure adds depth-dependent strip force, and marginal or probability models add weighted local contributions.
Draw a coordinate system, define the slice at a general position, express every changing factor in one variable, and state the domain and units.
Confusing mass density with weight density, measuring depth from the wrong reference, or integrating a marginal quantity without an initial value when a total function is requested.
Work in three passes
First, classify. Name the integral output and structural method before writing algebra. This separates a recognition error from a calculation error.
Second, solve without the key. Record a complete attempt, including bounds, constants, domains, units, or interpretation when the prompt asks for them.
Third, reveal one answer at a time. Compare the first line where your work differs, close the answer, and redo that item from a blank start.
Physics Application Studio
A compact set of standard models
For each situation, identify the local contribution, variable of integration, bounds, units, and final interpretation before evaluating.
A particle has velocity for . Find its displacement and total distance traveled, and explain how the sign changes affect the two totals.
Exercise 1 answer
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A spring requires of force at an extension of . Find the work required to stretch it from to beyond equilibrium.
Exercise 2 answer
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A rectangular tank is long, wide, and deep. It is full of water, which is pumped to an outlet above the top. Using water weight density , set up and evaluate the work.
Exercise 3 answer
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A triangular vertical plate has a top edge at the water surface and a vertex below the surface. Using water weight density , find the hydrostatic force.
Exercise 4 answer
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A rod occupies and has linear density , where . Find its mass, first moment about the origin, and center of mass.
Exercise 5 answer
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Force-position data are , , , , and newtons. Estimate the work from to meters with the Trapezoidal Rule and state the units.
Exercise 6 answer
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