The displacement(in metres) of a particle moving along x-axis is given by x=18t+5t^2.Calculate: i)instantaneous velocity at t=2s ii)instantaneous acceleration.

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The displacement(in metres) of a particle moving along x-axis is given by x=18t+5t^2.Calculate: i)instantaneous velocity at t=2s ii)instantaneous acceleration.

Given =

x = 18t + 5t²

Asked =

1.) Instantaneous Velocity at t = 2s

2.) Instantaneous Acceleration.

Answer =

1.) Instantaneous Velocity at t = 2s

displaystyle v(t) = frac{dx}{dt}\\v(t) = frac{d}{dt}(18t+5t^2)\\v(t) = 18 + 10t

so, when the t = 2s , the velocity will be

displaystyle v(2) = 18 +10.2 \v(2) = 18 + 20 \v(2)= 38 text{ m/s}

2.) Instantaneous Acceleration

displaystyle a = frac{dv}{dt}\\a = frac{d}{dt}(18+10t)\\a = 10 text{ m/s}^2