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3rd Equation of Motion

A particle st...

Question

A particle starts from rest with constant acceleration. The ratio of speed attained by a particle at $t = 1 s, 2 s, 3 s . . . . . . . . .$ will be:

1 : 3 : 5 . . . . . . . .

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1^{2} : 3^{2} : 5^{2} : . . . . . . . . . . .

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(1 - \sqrt{2}) : (\sqrt{2} \sqrt{3}) : (\sqrt{3} - \sqrt{4}) . . . . . . .

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1 : 2 : 3 . . . . . . .

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Solution

The correct option is D $1 : 2 : 3 . . . . . . .$

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For a body starting from rest and moving with uniform acceleration, the ratio of the distances covered for 1s, 2s, 3s, ..... is

t = 0

The position of a particle travelling along x - axis is given by $x_{t}$ = $t^{3}$ - 9 $t^{2}$ + 6t where $x_{t}$ is in m and t is in second . Then

1) the particle does not come to rest at all.

2) the particle comes to rest firstly at (3 - $\sqrt{7}$ ) s and then at (3 + $\sqrt{7}$ ) s

3) the speed of the particle at t= 2s is 18 m $s^{- 1}$

4) the acceleration of the particle at t= 2s is 6 m $s^{- 2}$

t = 0

(- 1, 0)

x -

v = 3 t^{2} + 2 t m/s

a = 3 t^{2} {m s}^{- 2}

t = 0

1 {m s}^{- 1}

t = 2 s

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