An object moves with velocity v (t) = t^2-8t+7

a) write a polynomial expression for the position of the particle at any time t greater or equal to zero.

b) at what time (s) is the particle changing direction

c) find the total distance traveled by the particle from t=0 and t=4

a) write a polynomial expression for the position of the particle at any time t greater or equal to zero.

Position is found by integrating velocity:

s (t) = (t^3) / 3 - 4t^2 + 7t + c

where c is a constant corresponding to the position at t=0.

b) at what time (s) is the particle changing direction

the particle changes direction whenever the velocity is zero; the velocity function equals

(t-1) (t-7) a difference of squares so the zeros are 1 and 7, it changes direction at 1 second and 7 seconds.

c) find the total distance traveled by the particle from t=0 and t=4

s (0) = c

s (1) = 8/3 + c

s (4) = 64/3 - 64 + 28 + c.

from 0 to 1 the particle travels 8/3 units. From 1 to 4 it travels - (64/3 - 36 - 8/3) = ( - (56/3 - 108/3))

= - (-52/3) = 52/3 units

so in total it travels 52/3 + 8/3 = 20 units