Posted by kriti on .
a particle moves along the y axis so that its position at any time t, for 0 is less than or equal to t which is less than or equal to 5, is given by y(t)=t^418t^2. in which intervals is the particle speeding up?

calculus 
bobpursley,
y'=4t^336t= 4t(t^29)=4t(t+3)(t3)
y"=12t^236=12(t^23)=12(t+sqrt3)(tsqrt3)
so when t=less than sqrt3, y"=+ * or negagive, slowing down.
t= greater than sqrt3, y"=+ * + speeding up.