MCQ
A particle has an initial velocity of ($3\hat i + 4\hat j)\;ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j)\;ms^{-1}$ Its speed after $10\;s$ is:
- A$7 $ unit
- B$8.5$ unit
- C$10$ unit
- ✓$7\sqrt 2 $ unit
✓
Answer
Correct option: D.
$7\sqrt 2 $ unit
d
$\begin{array}{l}
Given\,\vec u = 3\hat i + 4\hat j,\hat a = 0.4\hat i + 0.3\hat j,t = 10s\\
\vec v = \vec u + \vec at = 3\hat i + 4\hat j + \left( {0.4\hat i + 0.3\hat j} \right) \times 10\\
= 7\hat i + 7\hat j\\
\therefore \left| {\vec v} \right| = \sqrt {{7^2} + {7^2}} = 7\sqrt 2 \,units
\end{array}$
$\begin{array}{l}
Given\,\vec u = 3\hat i + 4\hat j,\hat a = 0.4\hat i + 0.3\hat j,t = 10s\\
\vec v = \vec u + \vec at = 3\hat i + 4\hat j + \left( {0.4\hat i + 0.3\hat j} \right) \times 10\\
= 7\hat i + 7\hat j\\
\therefore \left| {\vec v} \right| = \sqrt {{7^2} + {7^2}} = 7\sqrt 2 \,units
\end{array}$
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