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AIIMS 2017
Exam
AIIMS
Year
2017
Subject
Physics
Chapter
Motion in One Dimension

AIIMS 2017 · Physics · Motion in One Dimension

Assertion : If a=-2 t for a particle moving in a straight...

Assertion : If a=−2ta=-2 t for a particle moving in a straight linestartingwithan initialvelocity 4 m/s4 \mathrm{~m} / \mathrm{s} from the origin, then distance travelled by it in 2 s2 \mathrm{~s} is same as displacement. Reason : Velocity changes direction after 2 s2 \mathrm{~s} only.

Options

  1. AIf both assertion and reason are true and reason is the correct explanation of assertion.
  2. BIf both assertion and reason are true but reason is not the correct explanation of assertion.
  3. CIf assertion is true but reason is false.
  4. DIf both assertion and reason are false.

Correct answer

B. If both assertion and reason are true but reason is not the correct explanation of assertion.

Step-by-step solution

a=−2ta=-2 tdvdt=−2t or ∫4vdv=−2∫0ttdtv−4=−t2 or v=4−t2⇒v>0 for t<2,v=0 for t=2,v<0 for t>2\begin{aligned} & \frac{d v}{d t}=-2 t \text{ or } \int_4^v d v=-2 \int_0^t t d t \\ & v-4=-t^2 \text{ or } v=4-t^2 \\ & \Rightarrow \quad v>0 \text{ for } t < 2, \\ & \quad v=0 \text{ for } t=2, \\ & v < 0 \text{ for } t>2\end{aligned}$ThebodyreversesitsdirectionofmotionafterThe body reverses its direction of motion after2\mathrm{ s}.$
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