Question

v=2t. Find speed at 3sec. If at t=0 body is 2m behind origin. ​

Answer 1

Answer:

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Speed = 7 m

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Explanation:

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Given:

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• V = 2t
• Body is 2 m behind origin.

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To find:

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S at 3s if at t = 0

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Solution:

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S = $\displaystyle\int$ vdt = $\int$ 2tdt

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= 2$\displaystyle\int$ tdt

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$= \frac{2t {}^{2} }{2} \\ \\ = t {}^{2} + c$

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S = t$^{2}$ + C

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Now put S = – 2, we get

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– 2 = 0$^{2}$ + C

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$\implies$ C = – 2

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S = t$^{2}$ – 2

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$\implies$ S = 3$^{2}$ – 2 ⠀⠀⠀ [$\because$ t = 3]

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$\implies$ S = 9 – 2

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= 7 m

Answer 2

Answer:

The speed is 9 m/s.

Explanation:

• The given relation between velocity and time is v = 2t.

The motion of any body is continuous. So distance, S = ∫ v dt

                                                                                         = ∫ 2t dt

                                                                                         = t² + C

            Here C is integration constant.

• The given condition is at t = 0 second S = 2 m behind the origin

                                                 S = - 2 m

        From the above relation, S = t² + C

                                                  -2 = 0² + C

                                                   C = -2

    So, the relation between distance and time is, S = t² - 2

• When time, t = 3 second distance covered S = 3² - 2 = 7 m

• The speed at   t = 3 second is = v = 3t = 3 × 3 = 9 m/s

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