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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Motion in One Dimension

NEET 2012 · Physics · Motion in One Dimension

A particle has initial velocity (2 i+3 j) and acceleration (0.3...

A particle has initial velocity (2i+3j)(2 \mathbf{i}+3 \mathbf{j}) and acceleration (0.3i+0.2j)(0.3 \mathbf{i}+0.2 \mathbf{j}). The magnitude of velocity after 10 s10 \mathrm{~s} will be

Options

  1. A929 \sqrt{2} units
  2. B525 \sqrt{2} units
  3. C5 units
  4. D9 units

Correct answer

B. 525 \sqrt{2} units

Step-by-step solution

Here, u⃗=2i^+3j^, a⃗=0.3i^+0.2j^,t=10s As vˉ=uˉ+a⃗tvˉ=(2i^+3j^)+(0.3i^+0.2j^)(10)=2i^+3j^+3i^+2j^=5i^+5j^∣v⃗∣=(5)2+(5)2=52 units \begin{aligned} & \text{Here, } \vec{u}=2 \hat{i}+3 \hat{j} \text{, } \\ & \vec{a}=0.3 \hat{i}+0.2 \hat{j}, t=10 \mathrm{ s} \\ & \text{ As } \bar{v}=\bar{u}+\vec{a} t \\ & \bar{v}=(2 \hat{i}+3 \hat{j})+(0.3 \hat{i}+0.2 \hat{j})(10) \\ & =2 \hat{i}+3 \hat{j}+3 \hat{i}+2 \hat{j}=5 \hat{i}+5 \hat{j} \\ & |\vec{v}|=\sqrt{(5)^2+(5)^2} \\ & =5 \sqrt{2} \text{ units } \end{aligned})$
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