Question
A particle has initial velocity $(2\hat i + 3\hat j ) $ and has acceleration $(0.3\,\hat i + 0.2\,\hat j)$ . Its speed after $10\,s$ is
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Answer
Here,
Initial velocity, $\bar{u}=2 \hat{i}+3 \hat{j}$
Acceleration, $\bar{a}=0.3 \hat{i}+0.2 \hat{j}$
Time , $t=10 s$
Let $\bar{v}$ be velocity of a particle after $10 s .$
Using, $\bar{v}=\bar{u}+\bar{a} t$
$\therefore \bar{v} =(2 \hat{i}+3 \hat{j})+(0.3 \hat{i}+0.2 \hat{j})$
$ =2 \hat{i}+3 \hat{j}+3 \hat{i}+2 \hat{j}=5 \hat{i}+5 \hat{j}$
Speed of the particle a fter $10 s=|\bar{v}|$
$=\sqrt{(5)^2+(5)^2}=5 \sqrt{2} \text { units }$
Initial velocity, $\bar{u}=2 \hat{i}+3 \hat{j}$
Acceleration, $\bar{a}=0.3 \hat{i}+0.2 \hat{j}$
Time , $t=10 s$
Let $\bar{v}$ be velocity of a particle after $10 s .$
Using, $\bar{v}=\bar{u}+\bar{a} t$
$\therefore \bar{v} =(2 \hat{i}+3 \hat{j})+(0.3 \hat{i}+0.2 \hat{j})$
$ =2 \hat{i}+3 \hat{j}+3 \hat{i}+2 \hat{j}=5 \hat{i}+5 \hat{j}$
Speed of the particle a fter $10 s=|\bar{v}|$
$=\sqrt{(5)^2+(5)^2}=5 \sqrt{2} \text { units }$
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