If the vector components of the position of a particle moving in the xy plane as a function of time are x = (2.7 m/s2)t2i and y = (5.1 m/s3)t3j, at what time t is the angle between the particle's velocity and the x axis equal to 45°?

Time: 0.35 s

Explanation:

The position vector of the particle is

where the first term is the x-component and the 2nd term is the y-component.

The particle's velocity vector is given by the derivative of the position vector, so:

The particle's velocity has an angle with the x-axis of 45 degrees when the x and the y component have same magnitude. Therefore:

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