1. During the time period from t=0 to t=6 seconds, a particle moves along the given by

X(t) = 3cos(∏t) and y(t)= 5sin(∏t).

a) Find the position of the particle when t= 2.5

b) On the axes provided below, sketch the graph of the path of the particle from t=0 to t=6. Indicate the direction of the particle along its path.

c) How many times does the particle pass through the point found in part a.

d) Find the velocity vector for the particle at any time t.

e) Write and evaluate an integral expression, in terms of sine and cosine, that gives the distance the particle travels from t= 1.25 to t= t.75.

X(t) = 3cos(∏t) and y(t)= 5sin(∏t).

a) Find the position of the particle when t= 2.5

b) On the axes provided below, sketch the graph of the path of the particle from t=0 to t=6. Indicate the direction of the particle along its path.

c) How many times does the particle pass through the point found in part a.

d) Find the velocity vector for the particle at any time t.

e) Write and evaluate an integral expression, in terms of sine and cosine, that gives the distance the particle travels from t= 1.25 to t= t.75.

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