Vault Of Euclid

Finding When a Particle Changes Direction

Rectilinear and curvilinear motion warmup

A particle moving on a line is at position \( s = t^3 - 6t^2+9t-4 \) at time \( t \). At which time(s) \( t \), if any, does it change direction?

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What you need first

Power rule for differentiation
Factoring quadratic equations
Understanding the relationship between position and velocity

What this problem tests

Tests the ability to differentiate a polynomial, factor a quadratic, and interpret the sign changes of a derivative in a physical context.

This is a standard introductory calculus problem demonstrating the physical interpretation of the first derivative.

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