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AIIMS 2014
Exam
AIIMS
Year
2014
Subject
Physics
Chapter
Motion in One Dimension

AIIMS 2014 · Physics · Motion in One Dimension

A particle is moving eastwards with a velocity of 5 ~m / s . In 10...

A particle is moving eastwards with a velocity of 5 m/s5 \mathrm{~m} / \mathrm{s}. In 10 s10 \mathrm{~s}, the velocity changes to 5 m/s5 \mathrm{~m} / \mathrm{s} northwards. The average acceleration in this time isA particle is moving eastwards with a velocity of 5 ~m / s . In 10 ~s , the velocity changes to 5 ~m / s northwards.

Options

  1. Azero
  2. B12 m s−2\frac{1}{\sqrt{2}} \mathrm{~m} \mathrm{~s}^{-2} towards north-west
  3. C12 m s−2\frac{1}{\sqrt{2}} \mathrm{~m} \mathrm{~s}^{-2} towards north-east
  4. D12 m s−2\frac{1}{\sqrt{2}} \mathrm{~m} \mathrm{~s}^{-2} towards north

Correct answer

B. 12 m s−2\frac{1}{\sqrt{2}} \mathrm{~m} \mathrm{~s}^{-2} towards north-west

Step-by-step solution

Velocity in eastward direction =5i^=5 \hat{i} velocity in northward direction =5j^=5 \hat{j} A particle is moving eastwards with a velocity of 5 ~m / s . In 10 ~s , the velocity changes to 5 ~m / s northwards.
∴\therefore Acceleration a⃗=5j^−5i^10\vec{a}=\frac{5 \hat{j}-5 \hat{i}}{10} or a⃗=12j^−12i^\vec{a}=\frac{1}{2} \hat{j}-\frac{1}{2} \hat{i} or ∣a⃗∣=(12)2+(−12)2|\vec{a}|=\sqrt{\left(\frac{1}{2}\right)^2+\left(-\frac{1}{2}\right)^2} or ∣a⃗∣=12 m s−2|\vec{a}|=\frac{1}{\sqrt{2}} \mathrm{~m} \mathrm{~s}^{-2} towards north-west.
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