Question

the fisplacement od particle is 15t plus 25 find velocity at t= 2 sec​

Answer 1

Correct Question :

The displacement of a particle is 15t + 25 , Find the velocity at t = 2 sec

Given :

• Instantaneous displacement = 15t + 25

To Find :

• The velocity at t = 2 sec

Solution :

Differentiation of displacement of particle with respect to time gives us the velocity. Mathecmatically ,

$\\ \star \: {\boxed{\purple{\sf{v = \frac{dx}{dt} }}}}$

Substituting the values we have ,

$\\ : \implies \sf \: v = \frac{d}{dt} (15t + 25)$

$\\ : \implies \sf \: v = \frac{d}{dt} (15t) + \frac{d}{dt} (25)$

• Now using exponent rule of differentiation ,

$\\{\boxed{\sf{ \frac{d}{dx} ( {x}^{n} ) = n {x}^{n - 1} }}}$

$\\ : \implies \sf \: v = (15 \: \times 1t^{1 - 1} ) + \frac{d}{dt} (25)$

$\\ : \implies \sf \: v = (15 \times 1 {t}^{0} ) + \frac{d}{dt} (25)$

$\\ : \implies \sf \: v = (15 \times 1 \times 1) + \frac{d}{dt} (25)$

• Differentiation of a constant is zero.

$\\ : \implies \sf \: v = 15 + 0$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{v = 15 \: }}}}} \: \bigstar$

∴ At any given time the velocity of the given particle is 15 m/s.

Answer 2

Answer :-

➙ Velocity (v) $\leadsto$ $\boxed{\bold{\red{15m/s}}}$

$\:$

Given :-

• Displacement (x) = 15t + 25

• Time (t) = 2 sec

$\:$

To find :-

• Velocity (v)

$\:$

Formula used :-

• $\boxed{\sf{v = \dfrac{dx}{dt}}}$

• $\boxed{\sf{\dfrac{d}{dt}(t^{n}) = n.t^{n-1}}}$

$\sf{•\:Derivative\:of\:constant\:is\:‘0’.}$

$\:$

Solution :-

➪ $\sf{v = \dfrac{dx}{dt}}$

➪ $\sf{v = \dfrac{d}{dt} (15t +25)}$

➪ $\sf{v = \dfrac{d}{dt}(15t)+\dfrac{d}{dt}(25)}$

➪ $\sf{v = 15(1.t^{1-1})+ 0}$

➪ $\sf{v = 15(1)+ 0 =}$$\bold{\red{15m/s}}$