Question

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

Answer 1

Answer:

Instantaneous velocity=dx/dt

Instantaneous acceleration =

$\frac{ {d}^{2} x}{d {y}^{2} }$

Answer 2

Answer:

Instantaneous velocity=$\frac{dx}{dt}$

Acceleration ,a=$\frac{d^2x}{dt^2}$

Explanation:

We are given that  a motion of an object is described by

$x=f(t)$

We have to find the instantaneous velocity and acceleration

We know that

Instantaneous velocity=$\frac{ds}{dt}$

Therefore, instantaneous velocity=$\frac{dx}{dt}=\frac{df(t)}{dt}=f'(t)$

Hence, instantaneous velocity=f'(t)

Acceleration ,a=$\frac{d^2x}{dt^2}$

Substitute the values then we get

a=$\frac{d^2f(t)}{dt^2}=f''(t)$

Hence, the acceleration ,a=f''(t)