Need help with this question, dunno what to do. Please help me
The position function of an object that moves in a straight line is . Calculate the maximum and minimum velocities of the object over the given time interval.
Need help with this question, dunno what to do. Please help me
The position function of an object that moves in a straight line is . Calculate the maximum and minimum velocities of the object over the given time interval.
Velocity is ds/dt. So differentiate. Max and min values in the time interval will occur either at stationary points (set ds/dt=0, solve for t and sub to find s at these points). Also find s(0) and s(2) ie the end points. Then compare the values and pick the biggest and smallest.
note that for all values of t in the given interval .
to find the max and min velocity ...
at
for
and
for
therefore, is a maximum at
is the maximum velocity in the given interval.
the minimum velocity would occur at one of the two endpoint times ( or ) if they are included in the interval.
recheck the given interval to see if it is really .