Question

A body of mass m has its position x at a time 't' , expressed by the equation . The instantaneous force F on the body is proportional to $x=3t^{3/2}+2t+1/2$. The instantaneous force F on body is proportional to

• A. $t^{3/2}$
• B. $t$
• C. $t^{-1/2}$
• D. $t^0$

Answer 1

The correct option is C $t^{-1/2}$

$\begin{array}{c}x=3t^{\frac{3}{2}}+2t+\frac{1}{2}\\ V=\frac{dx}{dt}=\frac{9}{2}{t}^{\frac{1}{2}}+2\\ a=\frac{dv}{dt}=\frac{9}{4}{t}^{\frac{-1}{2}}\\ a=\frac{9}{4}{t}^{\frac{-1}{2}}\\ F=m\times a\\ F\times t^{\frac{-1}{2}}\end{array}$ {C}