Justification is important for me to study.

1) Suppose that an object moving along a straight line has position function s(t) = = cos( at) + 2 sin(at) in meters, with t measured in hours. a) (2 points) Show that the velocity function, v(t), is equal to v(t) = 5t cos(it). b) (4 points) Explain what v(+) d't represents and find its value on the interval [0, 2). (Don't forget units.) VALUE : c) (2 points) Circle ALL the correct statements about the function s, or write "NONE". A . s ( t ) = 2 + / v ( t ) at C. s( t ) = ( v ( x ) dx E. s(t) = s(0) + v(x) dx B. s( t ) = 2 + / v( x ) dx D. s(t ) - s(0 ) = w(x )dx F. s( t ) = s(0 ) + / v ( x ) dxd) (3 points) Write the integral that gives the displacement of the object during the time interval [0, 2], then calculate the displacement. (Hint: You were given a formula for s(t) above.) Integral: Displacement: e) (6 points) Write the integral that gives the distance traveled by the object during the time interval [0, 2), then calculate the distance traveled. Integral: Distance traveled:2) Evaluate each of the following. Explain and show your work. a) (3 points) [ S. " 2t cos(e ") de VALUE: b) (4 points) dx 2x cos( e " ) dx VALUE: c) (6 points) du Jo Ve+3 VALUE