Question

the displacement of a particle is represented by the following equation s=3t^2+7t^2+5t+8 where s is in metres and t in s . the acceleration of the particle at t=1s is

Answer 1

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Answer 2

The require answer is 26 m/$s^{2}$.

As per the question we need to find the acceleration of the particle.

The given is the displacement of a particle is represented by the following equation s=3t^2+7t^2+5t+8 where s is in metres and t in s.

we know that the second order derivative of the equation of the particle displacement is the acceleration of the particle at t time.

Therefore

We derivative of s with respect to the t.

$\frac{ds}{dt}$ = $6t^{2} + 14t + 5$

This is the velocity of the particle

u =  $6t^{2} + 14t + 5$

Now we derivative the u with respect to the t.

$\frac{du}{dt}$ = $12t + 14$

i.e a =  $12t + 14$

The given is t = 1 sec

Therefore

a = 12 . 1 + 14

   = 26 m/$s^{2}$

Hence the require answer is 26 m/$s^{2}$.

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