Velocity and Acceleration: Quiz

Problem 2

A point moves along the x axis so that its position x at time t is specified by the function

x(t) = sin(2πt)

At what time t > 0 does the point change direction? Give the smallest positive t.

Answers, problem 2

The point changes direction when its velocity is 0. dx/dt = 2πcos(2πt)

Equating dx/dt to 0, cos(π/2) = 0 so we can equate 2πt to π/2

t = 0.25

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