Respuesta :
Answer:
Step-by-step explanation:
Given that at time t, the position of a body moving along the s-axis is sequalsnegative t cubed plus 15 t squared minus 72 t m
i.e. [tex]s(t) = -t^3+15t^2-72 t[/tex]
Velocity is nothing but s'(t) = derivative of s
and acceleration is s"(t) = derivative of v(t)
[tex]v(t) = -3t^2+30t-72\\=-3(t^2-10t+24)\\= -3(t-6)(t-4)[/tex]
a) v(t) =0 when t = 4 or 6
b) [tex]a(t) = -6t+30[/tex]
a(t) =0 when t =5
c) Distance travelled by the body from 0 to 5 would be
[tex]s(5)-s(0)\\= -5^3+15(5^2)-72(5)\\= -125+375-360\\=-110[/tex]
i.e. 110 miles (distance cannot be negative)
