If rho(x, y) is the density of a wire (mass per unit length), then

m=∫crho(x, y)ds

is the mass of the wire. find the mass of a wire having the shape of a semicircle x=1+cos(t),y=sin(t), where t is on the closed interval from 0 to π, if the density at a point p is directly proportional to the distance from the y−axis and the constant of proportionality is 3. round in the tenths place.

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Explanation:

With the given information we have:

the interval is

now the mass has the given expression:

we will use the formula for a line integral and let:

therefore we have:

we solve the integral:

we're given that v₀ = 0 and a = 5.4 m/s². therefore, since v = at + v₀ for constant acceleration the equation for velocity is

after 28s,

m/s

which i would round to 150 m/s as my final answer