Question

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

Answer 1

Answer:

The velocity is 8 m/s and acceleration is 8 $m/s^{2}$

Explanation:

The motion of the particle is given by:

                                       $v^{3}$=$x^{3\\}$

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

substitute x= 8m,

                                    v= 8 m/s

Now differentiate it with respect to time (t),

                         $\frac{dv}{dt}$ = $\frac{dx}{dt}$

                   or,  $\frac{dv}{dt}$ = v

                   ∴  $\frac{dv}{dt}$ =  v

now substitute the value of v from equation 1,

                       $\frac{dv}{dt}$ = x              

now at, x= 8

                        $\frac{dv}{dt}$  = 8

                     ∴ $\frac{dv}{dt}$  = 8 $m/s^{2}$

As

                        $\frac{dv}{dt}$  = acceleration

So the acceleration of the particle at x=8m is 8 $m/s^{2}$ .