Question

Displacement in meters of a particle moving along x-axis is given by x=2t + 5t² the instantaneous velocity and instantaneous acceleration at t =2 seconds, respectively......​

Answer 1

$\sf x=2t+5t^2 \\\\\sf </p><p>Instantaneous \: velocity(dv) = \frac{dx} {dt} \\\\\sf </p><p>\frac{d(2t+5t^2)}{dx} \\\\\sf </p><p>= 2+10t \\\\\sf </p><p>When \: t=2s, \\\\\sf </p><p>Instantaneous \: velocity \: (dv) = 2+20 =22 m/s \\\\\sf </p><p>Now, \: Instantaneous \: acceleration \: = \frac{dv} {dt} \\\\\sf = \frac{d(2+10t)}{dt} \\\\\sf </p><p>= 0+10= 10 ms^{-2}</p><p>$