Question

Which would require a greater force, accelerating a $2kg$ mass at $5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$ or a $5kg$ mass at$3\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$?

Answer 1

Condition 1:-

Step 1:- Given data,

$$\begin{gathered} m_1=2kg \\ {a}_1=5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

Step 2:- Formula,

$$\begin{gathered} Force=mass\times acceleration \\ F=m\times a \end{gathered}$$

Step 3:- Finding the quantity of force,

$$\begin{gathered} \Rightarrow F_1=m\times a \\ \Rightarrow F_1=2\times 5 \\ \Rightarrow F_1=10\raisebox{1ex}{$kgm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.orN \end{gathered}$$

Condition 2:-

Step 1:- Given data,

$$\begin{gathered} m_2=5kg \\ {a}_2=3\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

Step 2:- Formula,

$$\begin{gathered} Force=mass\times acceleration \\ {F}_2=m_2\times a_2 \end{gathered}$$

Step 3:- Finding the quantity of force

$$\begin{gathered} \Rightarrow F_2=m\times a \\ \Rightarrow F_2=5\times 3 \\ \Rightarrow F_2=15\raisebox{1ex}{$kgm$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

As we can observe $F_2$is greater than$F_1$, therefore condition 1 requires more force as compared to condition 2.