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The position of a particle x (in metre) at a time t second is given by the relation r  = (3tiˆ - t 2 ˆj + 4kˆ) . Calculate the magnitude of velocity of the particle after 5s. the magnitude of velocity of the particle after 5s.
  • a)
    3.55 m/s
  • b)
    5.03 m/s
  • c)
    8.75 m/s
  • d)
    10.44 m/s
Correct answer is option 'D'. Can you explain this answer?
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The position of a particle x (in metre) at a time t second is given by...
Given: r = (3ti - t^2j - 4k)

To find: Magnitude of velocity after 5 seconds

Step 1: Find velocity vector by differentiating r with respect to time

v = dr/dt = (3i - 2tj) m/s

Step 2: Find the velocity at t=5s

v(5) = (3i - 2(5)j) m/s = (3i - 10j) m/s

Step 3: Find the magnitude of velocity

|v| = sqrt((3)^2 + (-10)^2) = 10.44 m/s

Hence, the correct option is (d) 10.44 m/s
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The position of a particle x (in metre) at a time t second is given by the relation r = (3tiˆ - t 2 ˆj + 4kˆ) . Calculate the magnitude of velocity of the particle after 5s.the magnitude of velocity of the particle after 5s.a)3.55 m/sb)5.03 m/sc)8.75 m/sd)10.44 m/sCorrect answer is option 'D'. Can you explain this answer?
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