Question

A $4 \,kg$ object has a velocity, $3.0\, \hat{ i }\, m / s$ at some instant. Eights seconds later, its velocity is $(8.0 \,\hat{ i }+10.0\, \hat{ j }) \,m / s$. Assuming that the object is subjected to a constant net force, the magnitude of the force is

• A. $\frac{5 \sqrt{5}}{2} N$
• B. $\frac{5 \sqrt{3}}{8} N$
• C. $\frac{8 \sqrt{5}}{3} N$
• D. $\frac{10 \sqrt{3}}{7} N$

Answer 1

Answer: (A)

$\frac{5 \sqrt{5}}{2} N$

Answer 2

Given, mass of an object, $m=4 \,kg , u =3 i \,m / s$
$v =(8 \hat{ i }+10 \hat{ j }) m / s$ and time $t=8 \,s$
As we know, equation of the motion
$v = u + a t$
$\Rightarrow \, 8 \hat{ i }+10 \hat{ j }=3 \hat{ i }+ a \times 8$
$\Rightarrow \, a =\frac{1}{8}(5 \hat{ i }+10 \hat{ j }) m / s ^{2}$
So, force $F =m a$
$F =\frac{4}{8}(\hat{ i }+10 \hat{ j })=\frac{1}{2}(\hat{ i }+10 \hat{ j }) N$
$\Rightarrow\, F=\frac{1}{2} \sqrt{5^{2}+10^{2}}$
$=\frac{5 \sqrt{5}}{2} \,N$