question_answer 47)

                  A body of mass 2kg travels according to the law                 \[x(t)=pt+q{{t}^{2}}+r{{t}^{3}}\] where \[p=3\,m{{s}^{-1}},\,q=4\,m{{s}^{-2}}\]and \[r=5\text{ }m{{s}^{3.}}\]                 The force acting on the body at \[t=2\] seconds is                 (a) 136 N                              (b)) 134 N                 (c) 15 8 N                             (d) 68 N

Answer:

                  (a) \[x(t)=pt+q{{t}^{2}}\text{+ }r{{t}^{3}}\]                 \ \[\upsilon (t)=p+2qt+3r{{t}^{2}}\]                 and \[a(t)=2q+6rt\]                 \ \[a(t){{|}_{t=2}}=2\times 4+6\times 5\times 2=68\text{ }m{{s}^{2}}\]                 \ \[F=ma=2\times 68=136\text{ }N\]