Velocity and Acceleration: Quiz

Problem 3

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 its direction of acceleration? Give the smallest positive t.

Answers, problem 3

The point changes direction of acceleration when the change in rate of change of acceleration is 0. Rate of change acceleration is x^'''(x) = –8π³cos(2πt)

Equating x^'''(x) to 0, cos(π/2) = 0 so we can equate 2πt to π/2

t = 0.25

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