Kinematics Question 593
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} $ . it’s speed after 10 sec is
Options:
A) 7$ \sqrt{2} $ unit
B) 7 unit
C) 8.5 unit
D)10 unit
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \vec{u}=3\hat{i}+4\hat{j}\Rightarrow \text{u}x=3\text{ and }\text{uy=4} $
$ \vec{a}=0.4\hat{i}+0.3\hat{j}\Rightarrow \text{a}x=0.4$
$\text{ and }\text{ay}=0.3 $
$ \text{So, }{{V _{x}}}=ux+a _{x}t=3+0.4\times 10=3+4=7 $ .
$ {{V _{y}}}=\text{uy+}{{a _{y}}}t=4+0.3\times 10=4+3=7 $
$ \vec{V}=7\hat{i}+7\hat{j} $
$ \Rightarrow |\vec{V}|=\sqrt{7^{2}+7^{2}}=7\sqrt{2}\text{ unit} $
