Question

the displacement X of an object is given as afunctoin of time X = 2t + 3t ^ 2.calculat the instantaneous velocity of the object at 2secand

Answer 1

$\huge{\underline{\underline{\sf{Answer}}}}$

Displacement “x” of the object is defined by:

$\mathrm{x = 2t + 3t{}^{2} }$

Differentiating x w.r.t to t,we get:

$\sf{v = \frac{dx}{dt} } \\ \\ \implies \: \sf{v = \frac{d(2t + 3t {}^{2} )}{dt} } \\ \\ \implies \: \huge{\sf{v = 6t + 2}}$

Here,

The instantaneous velocity of the object is defined by the function: v = 6t + 2

Substituting t = 2,

$\implies \: \underline{\boxed{ \sf{v = 14ms {}^{ - 1} }}}$

The instantaneous velocity of the object at t=2s is 14m/s

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

The relation between time and displacement is given by:-

$\large{X = 2t + 3t^{2}}$

$\huge{\bold{\underline{Explanation:-}}}$

As we have to find instantaneous velocity we need to differentiate the given equation.

Now,

$\large{v = \frac{dx}{dt}}$

substituting the "X" value.

$\large{v = \frac{d (2t + 3t^{2})}{dt}}$

Now, differentiating w.r.t time.

$\large{v = 2 + 6t}$

Velocity at any instant of the object is given by v = 2 + 6t.

Instantaneous speed at t = 2 seconds.

substituting the t = 2s in equation

$\large{v = 2 + 6 \times 2}$

$\large{v = 2 + 12}$

$\large{v = 14 m/s}$

$\huge{\boxed{\boxed{v = 14 m/s}}}$

So, instantaneous speed is 14 m/s of the object.