A rectilinear motion of a particle is defined by v3=x3. determine the velocity and acceleration at x=8m

The velocity is 8 m/s and acceleration is 8

Explanation:

The motion of the particle is given by:

                                       =

                                  or, v= x .................................1

substitute x= 8m,

                                    v= 8 m/s

Now differentiate it with respect to time (t),

                          =

                   or,   = v

                   ∴   =  v

now substitute the value of v from equation 1,

                        = x              

now at, x= 8

                         = 8

                     ∴  = 8

As

                         = acceleration

So the acceleration of the particle at x=8m is 8 .