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Motion in A Straight Line question

2023 · 13 Apr · Shift 2 · Q44
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  5. /2023 · 13 Apr · Shift 2 · Q44

Motion in A Straight Line question

2023 · 13 Apr · Shift 2 · Q44

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1
The distance travelled by an object in time ttt is given by s=(2.5)t2s=(2.5) t^{2}s=(2.5)t2. The instantaneous speed of the object at t=5 s\mathrm{t}=5 \mathrm{~s}t=5 s will be:
  1. A
    5 ms−15 \mathrm{~ms}^{-1}5 ms−1
  2. B
    12.5 ms−112.5 \mathrm{~ms}^{-1}12.5 ms−1
  3. C
    62.5 ms−162.5 \mathrm{~ms}^{-1}62.5 ms−1
  4. D
    25 ms−125 \mathrm{~ms}^{-1}25 ms−1
View written solutionFree

Correct answer: D

  1. The distance travelled is given by s=2.5t2s = 2.5t^2s=2.5t2

  2. Instantaneous speed is the time derivative of distance: v=dsdtv = \frac{ds}{dt}v=dtds​

  3. Differentiate sss with respect to ttt: v=ddt(2.5t2)=2.5⋅2t=5tv = \frac{d}{dt}(2.5t^2) = 2.5 \cdot 2t = 5tv=dtd​(2.5t2)=2.5⋅2t=5t

  4. At t=5 st = 5\,\text{s}t=5s, v=5(5)=25 m s−1v = 5(5) = 25\,\text{m s}^{-1}v=5(5)=25m s−1

  5. Now check the options:

    • A: 5 m s−15\,\text{m s}^{-1}5m s−1
    • B: 12.5 m s−112.5\,\text{m s}^{-1}12.5m s−1
    • C: 62.5 m s−162.5\,\text{m s}^{-1}62.5m s−1
    • D: 25 m s−125\,\text{m s}^{-1}25m s−1

So, the correct option is: D\boxed{D}D​

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