I am going through a Cal1 class with harsh graders.

0. Please check if I did what the questions ask me to do.

1. Please check if all answers are correct.

2. Find out notation or algebra mistakes that can cause deduction points.

3. If you find where it requires more justification, please help me with that.

1) Suppose that an object moving along a straight line has position function s(t) = _ cos(it) + - sin(#t) 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). s(t) = = cos(it) + - sin(nt) Vet ) = ( - SAN CITE) . IF ) + = Sin(It ) + $ coscit ) . IT = S' ct) = V (t ) - IF BATHE ) + I SHATTIE ) + 5 t cas ( It ) Vct ) = 5t cos (xct ) m / hours b) (4 points) Explain what _v(t) d't represents and find its value on the interval [0, 2]. (Don't forget units.) Is average velocity from the interval a to 2 2-0 [* 5t cos cut ) at based off of part A , this = ( Juce, de = sces ) * [# @5(+1 ) + 5 6) Sin(72 ) O VALUE : c) (2 points) Circle ALL the correct statements about the function s, or write "NONE". A. s( t ) = 2 7 / v(t ) at C. s( t) = ( x ) dx E. s( 1 ) = s(0) + v(x ) dx B. s( t ) + v ( x ) dx D. s(t) - s( 0) = v(x)dx F. s( t ) = s(0) [ (x) dx traveled not a frod) (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.) ( d c t ) = J * ( * ) d xc displacement dets = J . 5. X. Cos ( 1. 20 ) ex d (2 ) = J 5. x. C+5 (TI x ) dic d ( 2 ) = 0 based off of part by 5 . X . COS ( 1. 30 ) 5 s t . cos ( It ) dt = 0 Integral: Displacement: the distance traveled. e) (6 points) Write the integral that gives the distance traveled by the object during the time interval [0, 2], then calculate distance net ) = S. I vax/ dx = S I t x Cos ( 1 x ) | dx n ( 2) = 1 5 x cos ( 1 x ) / dx n (2 ) = ] 5 x e-5 ( x) dx - / 1.5 . .5 5 x ers ( Tx ) dx + 5 x c-5 ( TX ) dx 5 71 - 10 + + 15 TT+ 10 27 2 2 7 2 S. 1 + * cos ( 1 X ) | dix Integral: 5 71- 10 + 10 15 TT+ 10 + 2 7 2 = J. I t x cos(1x) | dx Distance traveled : Jo IT2) Evaluate each of the following. Explain and show your work. a) (3 points) x [ 2t cos( e' ) dt const * ( constant value ) = 0 O VALUE: b ) (4 points ) # 2x cos( e " ) [2 x cos ce s ] " nce> ( 2 ( In( ) ) . cosce " ( ) , ) - ( 26 . ) . cos ce") )= VALUE: - 2 ( IT ) . Cos (1) 5420 c) (6 points) Vedw + 3 du 9 + 3 9 Au 5e (revised ) dx = 4e du e * + 3 4 lack ] 4 40 = et du 5 = S - - dx 5 2 VALUE