Question
A particle has an initial velocity $$3\hat i + 4\hat j$$ and an acceleration of $$0.4\hat i + 0.3\hat j.$$ Its speed after $$10\,\sec $$ is
A.
$$7\sqrt 2 \,units$$
B.
$$7\,units$$
C.
$$8.5\,units$$
D.
$$10\,units$$
Answer :
$$7\sqrt 2 \,units$$
Solution :
$$\eqalign{
& \vec u = 3\hat i + 4\hat j \Rightarrow ux = 3\,\,{\text{and}}\,\,uy = 4 \cr
& \vec a = 0.4\hat i + 0.3\hat j \Rightarrow ax = 0.4\,\,{\text{and}}\,\,ay = 0.3 \cr
& {\text{So, }}{V_x} = ux + {a_x}t = 3 + 0.4 \times 10 = 3 + 4 = 7 \cr
& {V_y} = uy + {a_y}t = 4 + 0.3 \times 10 = 4 + 3 = 7 \cr
& \vec V = 7\hat i + 7\hat j \cr
& \Rightarrow \left| {\vec V} \right| = \sqrt {{7^2} + {7^2}} = 7\sqrt 2 \,units \cr} $$