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The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

  • v0 + 2g + 3f

  • v0 + g/2 + f/3

  • v0 + g + f

  • v0 + g + f


B.

v0 + g/2 + f/3

integral subscript 0 superscript straight x space dx space equals space integral subscript 0 superscript 1 space left parenthesis straight V subscript 0 space plus space gt space plus ft squared right parenthesis space dt
straight x space equals straight v subscript 0 space plus space straight g space open parentheses 1 half close parentheses space plus straight f open parentheses 1 third close parentheses
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Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate.Assume that the duration of collision is negligible and the collision with the plate is totally elastic.Then the velocity as a function of time and the height as a function of time will be


C.

When ball strikes the surface its velocity will be reversed therefore correct answer is 3.

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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000. N/m. The spring compresses by

  • 5.5 cmYes

  • 2.5 cm

  • 11 cm

  • 11 cm


A.

5.5 cmYes

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A motorcycle starts from rest and accelerates along a straight path at 2 m/s2. At the straight point of the motorcycle, there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at 94% of its value when the motorcycle was at rest?

  • 49 m

  • 98 m

  • 147 m

  • 147 m


B.

98 m

straight V space equals space square root of 2 aS end root space equals space square root of 4 straight S end root
also comma space 94 space equals space 100 space open parentheses fraction numerator 330 minus straight V over denominator 330 end fraction close parentheses
rightwards double arrow fraction numerator 33 space straight x space 6 over denominator 10 end fraction space equals space square root of 4 straight S end root
rightwards double arrow straight S space equals 98 space straight m
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A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-directionn with a constant speed. The position of the first body is given by x1(t) after time ‘t’ and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x1 – x2)as a function of time ‘t’?


B.

straight x subscript 1 space left parenthesis straight t right parenthesis space equals space 1 half space at squared
straight x subscript 2 space left parenthesis straight t right parenthesis space equals space vt
straight x subscript 1 minus straight x subscript 2 space equals space 1 half at squared space minus vt
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