Question

The displacement of a particle is given by x(t)=4t2 +8t meter. Its velocity at t = 10 second is
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Answer 1

Given :

Displacement of the particle , x(t) = 4t² + 8t m

To find :

velocity of the particle at t = 10s

Concept :

Instantaneous Velocity

The velocity of particle at a particular instant of time is called it's instantaneous Velocity

lf ∆S is the distance by a particle in a time interval ∆t then,

average velocity = ${\sf{\dfrac{\Delta S}{\Delta t}}}$

If the time interval ∆t is chosen to be very small, i.e., as ∆t → 0, the corresponding velocity is called instantaneous velocity given by

${ \boxed{\sf{V_{ints} = Lt_{\Delta t \to 0} \dfrac{\Delta S}{\Delta t} = \dfrac{ds}{dt}}}}$

Solution :

As we know,

${ \leadsto{\bf{V= \dfrac{ds}{dt}}}}$

According to the question,

s = 4t² + 8t

we have to differentiate s

${\leadsto {\bf {v=\dfrac{d}{dt}(4t^2+8t\big)}}}$

${\leadsto {\bf {v=4(2t)+8(1)}}}$

${\leadsto {\bf {v=8t+8}}}$

according to Question,

t = 10

${\leadsto{\bf {v=8(10)+8}}}$

${\leadsto{\bf {v=80+8}}}$

${\leadsto{\bf {v=88 \: m/s}}}$

thus, the velocity of the particle at 10sec is 88m/s