Find the distance traveled by a particle moving along the x-axis given its position function involving a cubic term and a cosine term.

Vault Of Euclid

Distance Traveled by a Particle with Trigonometric Position

Rectilinear and curvilinear motion core

A particle moves along the \(x\)-axis according to the equation \( x = \frac{1}{3}t^3 - \frac{1}{2} \cos 2t + 3.5 \). Find the distance traveled between \( t=0 \) and \( t = \pi/2 \).

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What you need first

Differentiation of polynomials and trigonometric functions
The chain rule
Evaluating trigonometric functions at standard angles
Understanding the relationship between position, velocity, and distance

What this problem tests

Tests the ability to differentiate a position function, analyze the sign of the resulting velocity to check for changes in direction, and compute the net displacement.

This is a standard Calculus I problem on rectilinear motion, testing the distinction between displacement and total distance traveled.

Distance Traveled by a Particle with Trigonometric Position

What you need first

What this problem tests

More on Rectilinear and curvilinear motion