Rate of Change Questions? I have this equation for a rate of change problem below s = t 4 − 4 t 3 − 20 t 2 + 20 t , t ≥ 0The question asks meAt what time does the particle have a velocity of 20 m/s?How do i solve this? Basically what steps do I take to find at what time the particle has that velocity?

Question

Rate of Change Questions? I have this equation for a rate of change problem below  s  =      t    4    −  4      t    3    −  20      t    2    +  20  t  ,    t  ≥  0The question asks meAt what time does the particle have a velocity of 20 m/s?How do i solve this? Basically what steps do I take to find at what time the particle has that velocity?

seguidora1e · Accepted Answer

If s is the distance as a function of time t, then the velocity is given by   v  =                    d        s                    d        t            Set this derivative                     d        s                    d        t             to 20 and solve the cubic, with the constraint t&amp;gt;0, to get the value of t.Note that the cubic you obtain can be factored easily.Move your cursor over the gray area for the complete answer.                    d        s                    d        t              =  4      t    3    −  12      t    2    −  40  t  +  20Setting this to 20 gives us,  4      t    3    −  12      t    2    −  40  t  +  20  =  20    ⟹    4      t    3    −  12      t    2    −  40  t  =  0    ⟹    4  t  (      t    2    −  3  t  −  10  )  =  0This gives us  t  (  t  −  5  )  (  t  +  2  )  =  0Since t&amp;gt;0, we get that t=5.

Rate of Change Question I have this equation for a rate of change problem below s=t^4−4t^3−20t^2+20t,t>=0 The question asks me At what time does the particle have a velocity of 20 m/s? How do i solve this? Basically what steps do I take to find at what time the particle has that velocity?

Answered question

Answer & Explanation

New Questions in Calculus 2