Question

The displacement of a particle moving in straight line is given by x=2t²+t+5,where is expressed in metres and t in second .The acceleration at t=2sec is ​

Answer 1

Given:

Displacement of particle w.r.t. time:

$\rm x = ( 2 {t}^{2} + t + 5) \: m$

To Find:

Acceleration (a) of particle at t = 2 s

Answer:

Double differentiation of displacement-time relation gives acceleration:

$\bf \implies a = \dfrac{ {d}^{2}s }{d {t}^{2} } \\ \\ \rm \implies a = \dfrac{d }{dt}( \frac{ds}{dt}) \\ \\ \rm \implies a = \dfrac{d}{dt}( \dfrac{d}{dt}(2 {t}^{2} + t + 5)) \\ \\ \rm \implies a = \dfrac{d}{dt} (4t + 1) \\ \\ \rm \implies a = 4 \: m {s}^{ - 2}$

$\therefore$ $\boxed{\mathfrak{Acceleration \ of \ particle \ (a) = 4 \ m/s^2}}$