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AP Physics C: Mechanics
4.2 Change in Momentum and Impulse
AdvancedMCQMathematical20.8k
A horizontal line represents a frictionless surface with two labeled points at \(x = 0\) and \(x = L\). A small rectangular block labeled \(m\) rests at \(x = 0\). A single horizontal arrow originating from the right side of the block points to the right along the surface toward \(x = L\) and is labeled \(F(x) = \beta x^2\). A horizontal coordinate axis beneath the surface points to the right and is labeled \(x\). No other labels, lines, text, or axes appear.
A block on a frictionless surface subject to a position-dependent force.
A block of mass \(m\) is initially at rest at position \(x = 0\) on a frictionless horizontal surface. Starting at time \(t = 0\), a net horizontal force with magnitude \(F(x) = \beta x^2\) is applied to the block in the \(+x\)-direction, where \(\beta\) is a positive constant. Which of the following integrals correctly represents the magnitude of the impulse delivered to the block as it travels from \(x = 0\) to \(x = L\)?

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