Calc
posted by Aparna on .
A particle moves along the xaxis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3  3t^2 +8
A) show that at time t= 0 the particle is moving to the right.
B) find all values of t for which the particle is moving to the left.
C) what is the position of the particle at time t=3
D) when t=3, what is the total distance the particle has traveled

x = 1/3t^3  3t^2 + 8
dx/dt = t^2  6t
a)
when t=0 ,
dx/dt = 00 = 0
showing that x is not moving at all at that time.
b) to be moving to the left
t^2  6t < 0
t(t6) < 0
which is true for all
0 < t < 6
c) when t=3
x = (1/3)(27)  3(9) + 8 = 10
d) when t= 0 , x = 8
when t=3 , x = 10
the particle has traveled 18 units