Question

The velocity of a function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval.
v(t)=t^2-2t-8, [1,6]

Answer 1

velocity = ds/dt

so oyu need to integrate the equation for v to give an equation for s (displacement)

Now - normally you would need constant of integration and some way of determining it, however since the question asks for change between two values, then the constant will subtract out.

The displacement is given by (value at t = 6)-(value at t-1) so simply substitute the values into your equation for s, then subtract.

The distance travelled includes changes of direction, normally given by the solution to v=0

you have the equation for v - solve it for v=0

If any solution occurs within your interval then the direction has changed. You need to calculate distance travelled up to each change of direction, then add them together for total distance covered.