Question

The position of an object at any time t is given by s(t)=3t⁴- 40t³+126t²-9.
Find velocity at any time t?
Does the object ever stop changing ?
When is the object moving to left And when is object moving to right?

Answer 1

Answer:

velocity, v = ds(t)/dt = 12t.t.t - 120t.t - 252t

dv(t)/dt = 36t.t - 240.t -252 which is not equal to zero. A acceleration never changes, So the object will never stop changing.

Solution of the second equation will be t1,t2 for which either the acceleration will be positive or negative.For positive, the object will move towards right and for negative case, it can move towards left direction.

Answer 2

The velocity at  time (t) is $V=( 12t^{3} - 120t^{2} +252t)$.

The object never stops changing.  

The object moves to the right at  positive  value of velocity V.

The object moves to the left at negative value of  velocity V.

Step-by-step explanation:

Given:

An object's position at  time (t)is given by  $s(t)=3t^{4} - 40t^{3} +126t^{2} -9.$

To Find:

The velocity at  time (t). The object ever stop changing.

The object moves to left.The object moves to  right.

Solution:

As given, An object's position at  time (t)is given by$s(t)=3t^{4} - 40t^{3} +126t^{2} -9.$  

 Velocity at  time (t),$V=\frac{d}{dt} s(t)$

                                     $=\frac{d}{dt}( 3t^{4} - 40t^{3} +126t^{2} -9)$

                                      $= 3\times 4t^{3} -40\times 3t^{2} +126\times2t-0$

                                      $= 12t^{3} - 120t^{2} +252t$

Thus, the velocity at any time (t) is $V=( 12t^{3} - 120t^{2} +252t)$.

The equation of  the velocity at  time (t)  $V=( 12t^{3} - 120t^{2} +252t)$ depicts an exponential equation which proves that the object never stops changing.

Thus, the object never stops changing.

The object moves to the right at positive value of velocity V.

Thus,the object moves to the right at  positive  value of velocity V.

The object moves to the left at  negative  value of velocity V.                                    

Thus,the object moves to the left at  negative  value of velocity V.

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