The velocity as a function of time is given as
v(t) = 2t−t2 in m/s and t in seconds (s). Consider the time interval from t=0 to t = 10 .
1. Find the time after t=0 when the particle changes direction.
2. Find the time before which the acceleration is positive.

Question

The velocity as a function of time is given as
v(t) = 2t−t2 in m/s and t in seconds (s). Consider the time interval from t=0 to t = 10 .
1. Find the time after t=0 when the particle changes direction.
2. Find the time before which the acceleration is positive.

campbell_st · Answer

ok... if you factor the velocity equation, you get the points where the velocity is zero.

the change in velocity occurs beyond the 2nd zero. 

the 1st derivative of the velocity equation will give the acceleration equation. 

the acceleration will change at the stationary point.... or the solution to the 1st derivative. 

the curve looks like 

|dw:1382335633998:dw|

hope this helps