Question

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

−(t + 1) sin(t2/2). At time t = 0, the particle is at position x = 1. Find the acceleration of the particle at time t = 4. Is the speed of the particle increasing at t = 4? Why or why not?
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Answer 1

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

Step-by-step 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