Question

A particle moves along the x axis so that its velocity at time t is given by v(t)=

Answer 1

Answer:

a = 0.7267 ,  acceleration is positive therefore the speed is increasing  

Explanation:

The definition of acceleration is

         a = dv / dt

they give us the function of speed

         v = - (t-1) sin (t² / 2)

         a = - sin (t²/2) -  (t-1) cos (t²/2)  2t / 2

         a = - sin (t²/2) - t (t-1)  cos (t²/2)

the acceleration for t = 4 s

          a = - sin (4²/2) - 4 (4-1) cos (4²/2)

          a = -sin 8 - 12 cos 8

remember that the angles are in radians

          a = 0.7267

the problem does not indicate the units, but to be correct they must be m/s²

We see that the acceleration is positive therefore the speed is increasing