A particle moves a long the  $x-$  axis. The function  $x\left(t\right)$  gives the particle's position at any time,  $t\ge0$  :  $x\left(t\right)=5t^2-12t+3.$  What is the particle's velocity  $v\left(t\right)$  at  $t=3$  seconds?

A particle moves a long the  $x-$ axis. The function  $x(t)$ gives the particle's position at any time,  $t≥0$  :   $x(t)=5t^2−12t+3.$  What is the direction of the particle's motion at  $t=3$  ?

A particle moves along the  $x-$  axis . The function  $x(t)$  gives the particle's position at any time  $t≥0$ ,  $x(t)=2t^2-3t+5$  . What is the particle's acceleration  $a(t)$  at  $t=1$  ?

A large stone is falling through a layer of mud. At time t
t seconds, the depth of the stone in metres below the surface is given by:  $x\left(t\right)\ =\ 20\ \left(1-e^{\frac{-t}{2}}\right)$  . What is $\frac{\text{d}v}{\text{d}t}$  ?

Given that the velocity  $v\left(t\right)$  of the particle is given by  $v\left(t\right)=\sin\ \left(\frac{\pi t}{2}\right).\$  If initially the particle has a no displacement. What is the position of the particle at time t=1?