Question

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 2 sin2(t), y = 2 cos2(t), 0 ≤ t ≤ 4

Answer 1

The distance traveled by the particle at the given time interval is 0.28 m.

Position of the particle at time, t = 0

The position of the particle at the given time is calculated as follows;

x = 2 sin2(t)

y = 2 cos2(t)

x(0) = 2 sin2(0) = 0

y(0) = 2 cos2(0) = 2(1) = 2

Position of the particle at time, t = 4

x = 2 sin2(t)

y = 2 cos2(t)

x(4) = 2 sin2(4) = 0.28

y(4) = 2 cos2(4) = 2(1) = 1.98

Distance traveled by the particle at the given time interval

d = √[(x₄ - x₀)² + (y₄ - y₀)²]

d =  √[(0.28 - 0)² + (1.98 - 2)²]

d = 0.28 m

Thus, the distance traveled by the particle at the given time interval is 0.28 m.

Learn more about distance here: brainly.com/question/23848540

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