1. A slingshot launches a stone vertically with an initial velocity of 400 ft/s

Question

1. A slingshot launches a stone vertically with an initial velocity of 400 ft/s from an initial height of 10 ft. Find the average velocity over time interval [2, 9]. (Assume g = 32 ft/s2)

2. A particle moving along a line has position s(t) = t4 32t2 m, at time t seconds. What is the farthest distance to the left of the origin attained by the particle?

3. Find a value of n such that y = xnex satisfies the equation xy' = (x 20)y.

4. Find an equation of the tangent to the graph of y = f'(x) at x = 1 when f(x) = x3 + 4x2 + 5x.

Explanation / Answer

1)a(t) =-32

v(t)=32 dt

v(t)=-32t +c

v(0)=400

400=0+c

c=400

v(t)=-32t +400

s(t)=-32t +400 dt

s(t)=-16t2+400t +c

s(0)=10

10=-0+0+c

c=10

s(t)=-16t2+400t +10

average velocity =[s(9)-s(2)]/(9-2)

average velocity =[(-16*92+400*9 +10)-(-16*22+400*2 +10)]/7

average velocity =224 ft/s

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