Answers to Velocity Worksheet 3 1

							                          Position, Velocity, and Acceleration Worksheet Answers

1. (a) v(t) = 3t2 – 6t + 2
       a(t) = 6t – 6
       v(0) = 2 v(2) = 2
       a(0) - -6 a(2) = 6

                           s (2) − s (0)
   (b) average velocity:                 =0
                               2−0
         displacement: s(s) – s(0) = 0

2. (a)
                  −125 1875
          v(t ) =      + 4
                    t2    t
                  250 7500
          a (t ) = 3 − 5
                   t    t

         v(1) = 1750       v(5) = -2
         a(1) = -7250      a(5) = .4

                            s (5) − s (1)
   (b) average velocity:                  = 130
                                5 −1
         displacement: s(5) – s(1) = 520

3. (a) v(t) = 24 – 1.6t
       a(t) = -1.6
   (b) 15 seconds (when v(t) = 0)
   (c) 180 meters (find s(15))
   (d) 90 = 24t – 0.8t2
            T = 4.3934 seconds
   (e) 30 seconds (when s(t) – 0)

       Q(10) − Q(0)
4. (a)               = −10, 000 cu gal/min
           10 − 0
   (b) v(t) = -400(30 – t)
       V(10) = - 400 (20) = -8,000 cu gal/min

5. v(t) = 3t2 – 12t + 9
        = 3(t2 – 4t + 3)
        = 3(t – 1)(t – 3) = 0 when t = 1, 3

   a(1) = -6        a(3) = 6