velocity of a particle

Question

A particle moves along a straight line with velocity v in meters per second at time t seconds given by the formula: v(t)=t²-4t+3, where 0 is less than or equal to t which is less than or equal to 4.

a) Find the critical points and t intercepts for the function v.

b)Sketch the graph of the function v.

c) For what values of t is the velocity positive? Negative?

d) The displacement of the particle at an instant of time is the distance at that time of the particle from the staring point. Find the displacement at t=4 seconds.

e) Find the total distance traveled over the time interval from t=0 to t=4 seconds.

Answer 1

There is only one critical point at t=2.

The intercepts are at t=3 and t=1.

The graph is a parabola opening upward.On [0,4] the velocity is negative on (1,3) and positive elsewhere.

The displacement s(t) = integral of v(t)...but the problem gives no value for s(0)!