Question

Starting at t =0 , a particle moves away fom the origin of a worldwide system along th +ve x direction. Its position is a function of t and is given by x= 4t^3. Find the velocity and acceleration at time t = 2 sec.

Answer 1

$$\begin{gathered} x=4t^3 \\ velocityisgivenby: \\ v=\frac{dx}{dt} \\ v=4\times 3t^2 \\ v=12t^2 \\ att=2s \\ v=12\times 2\times 2=48/s \\ accelerationisgivenby: \\ a=\frac{dv}{dt}=\frac{d^{2}x}{d{t}^2} \\ a=12\times 2t \\ a=24t \\ att=2s \\ a=24\times 2=48m/s^2 \end{gathered}$$