Aparticle moves on a coordinate line with acceleration star tfraction d squared s over dt squared end fraction equals 60 start root t end root minus start fraction 21 over start root t end root end fraction , subject to the conditions that start fraction ds over dt end fraction equals 8 and sequals16 when t equals 1. find
a) the velocity v equals start fraction ds over dt endfraction in terms of t
b) the position s in terms of t.

Velocity , v (t) =  90√t³ -   42√t

Position , s (t) = 36 √t⁵ - 28√t³

Step-by-step explanation:

d²s/dt =60√t -21/√t, (1)

Subject to:

ds/dt =8; 16 at t=1

Integrating equation (1) we have :

ds/dt = 90√t³ -   42√t (2)

s = ∫90√t³ -   42√t dt

 =      36 √t⁵ - 28√t³ (3)

Velocity , v (t) =  90√t³ -   42√t

Position , s (t) = 36 √t⁵ - 28√t³

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

answer for #1 is c

answer for #2 is d

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