Question

A force of $1N$ acts on a body of mass of $10kg$. As a result, the body covers $100cm$ in $4seconds$ moving along a straight line. Find the initial velocity.

Answer 1

Step 1: Given data
The mass of the body $\left(m\right)=10kg$
Distance covered by the body $\left(s\right)=100cm=1m(Since100cm=1m)$
Time is taken by the body to cover the distance of $1m,t=4seconds$
Let the initial velocity of the body$=um/s$
Step 2: Using Newton's second law we get-
$$\begin{gathered} F=ma \\ F=Force \\ m=mass \\ a=acceleration \end{gathered}$$

$$\begin{gathered} s=ut+\frac{1}{2}a{t}^2 \\ s=dis\tan ce \\ u=initialvelocity \\ a=acceleration \\ t=time \end{gathered}$$

Step 3: Calculate the value of acceleration by substituting the value of force and mass.
$$\begin{gathered} 1N=\left(10kg\right)\times \left(a\right) \\ \Rightarrow a=\frac{1}{10} \\ a=0.1m{s}^{-2} \end{gathered}$$
Step 4: Calculate the value of the initial velocity $um/s.$
$$\begin{gathered} 1=u\left(4\right)+\frac{1}{2}(0.1)\times {\left(4\right)}^2 \\ 1=4u+8\times 0.1 \\ 1=0.8+4u \\ 1-0.8=4u \\ \Rightarrow u=\frac{1-0.8}{4} \\ u=\frac{0.2}{4} \\ u=0.05m{s}^{-1} \end{gathered}$$
Hence the initial velocity of the body is $0.05m{s}^{-1}$