Q.If the motion of an object is described by x = f(t), write the formulae for instantaneous velocity and acceleration.

[!TLDR] Both instantaneous velocity and acceleration are derivatives of position with respect to time. [!ANSWER] $v=\dfrac{dx}{dt} …

If the position of an object along a line is given as a function of time, $x=f(t)$, then by the definitions of sections 3.2 and 2 of this book, the instantaneous velocity is the first derivative of position with respect to time, $v = \dfrac{dx}{dt} = f'(t)$, and the instantaneous acceleration is the derivative of velocity with respect to time, which is equivalently the *se …

Apply the calculus definitions of instantaneous velocity (first derivative of position) and acceleration (second derivative of pos …

Forgetting that acceleration is the SECOND derivative of position, not the first — or writing it only as …