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Standard XII

Physics

Instantaneous Velocity

The motion of...

Question

The motion of a particle is described by the equation $x = a + b t^{2}$ where $a = 15 c m$ and $b = 3 c m / s e c^{2}$ . Its instantaneous velocity at time $3 s e c$ will be:

36 c m / s e c

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1 c m / s e c

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18 c m / s e c

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32 c m / s e c

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Solution

The correct option is C $18 c m / s e c$
Given $a = 15 c m b = 3 c m / s e c^{2} t = 3 s e c$
$x = a + b t^{2}$
Differentiating w.r.t t, we get
$\frac{d x}{d t} = 2 b t$
$v = 2 b t$
Substituting the values
$v = 2 \times 3 \times 3$
$v = 18 c m / s e c$

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The motion of a particle is described by the equation x=a+bt2 where a=15 cm and b=3 cm/sec2. Its instantaneous velocity at time 3 sec will be:

The correct option is C 18 cm/secGiven a=15 cmb=3cm/sec2t=3secx=a+bt2Differentiating w.r.t t, we getdxdt=2btv=2btSubstituting the valuesv=2×3×3v=18 cm/sec

The motion of a particle is described by the equation $x = a + b t^{2}$ where $a = 15 c m$ and $b = 3 c m / s e c^{2}$ . Its instantaneous velocity at time $3 s e c$ will be:

The correct option is C $18 c m / s e c$
Given $a = 15 c m b = 3 c m / s e c^{2} t = 3 s e c$
$x = a + b t^{2}$
Differentiating w.r.t t, we get
$\frac{d x}{d t} = 2 b t$
$v = 2 b t$
Substituting the values
$v = 2 \times 3 \times 3$
$v = 18 c m / s e c$