Vault Of Euclid

Analyzing Rectilinear Motion and Maximum Speed

Rectilinear and curvilinear motion core

A particle moves on a straight line so that its position \( s \) (in miles) at time \( t \) (in hours) is given by \( s = (4t-1)(t-1)^2 \). When is the particle moving to the right, when to the left, and when does it change direction? When the particle is moving to the left, what is the maximum speed that it achieves?
calculuskinematicsrectilinear-motionvelocityaccelerationspeedproduct-ruleoptimizationsecond-derivative-testcritical-pointsintervals-of-increase-and-decreasepolynomial-differentiation

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What you need first

What this problem tests

Tests the ability to relate position, velocity, and speed, and to apply optimization techniques to find maximum speed.

This is a standard application of derivatives in a first-semester calculus course, often found in chapters on applications of differentiation.

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