A particle of mass m, initially at rest at x = 0 isaccelerated by a force that i

Question

A particle of mass m, initially at rest at x = 0 isaccelerated by a force that increaces in time as F = Ct2. Determine its velocity v and posistion x as a function oftime. The book has no examples of what to do and we have not goneover this in class. I am lost. Thanks for your help. A particle of mass m, initially at rest at x = 0 isaccelerated by a force that increaces in time as F = Ct2. Determine its velocity v and posistion x as a function oftime. The book has no examples of what to do and we have not goneover this in class. I am lost. Thanks for your help.

Explanation / Answer

mass m = m Force F = C t^ 2 Accleration   a = F / m                      = Ct^ 2 / m velocity v = integral a   dt                = C t^ 3 / 3 m + C'            ----( 1) where C ' = integration constant Given at time t= 0 , velocity v = 0 because it startfrom rest substitue this in eq ( 1 ) we get 0 = 0 + C '                                               C ' = 0 eq( 1 ) becomes , v = Ct ^ 3 / 3m position   X = integral v dt                  = Ct ^ 4 / ( 4 * 3m ) + C "                 = C t ^ 4 / 12m + C"             ---( 2) where C " = integration constant Given at time t= 0 , X = 0 substitute this in eq ( 2 ) we get C " = 0 So, eq ( 2 ) becomes X = Ct^ 4 / 12 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.