Question

At time t>=0, the acceleration of a particle moving on the x-axis is a(t)=t+sin(t). At t=0, the velocity of the particle is -2. For what value of t will the velocity of the particle be zero?

Answer 1

Answer:

The velocity of the particle will be zero for  t = 1.47 sec .

Step-by-step explanation:

Given equation:

                                           a(t)=t+sin(t)

lets integrate it with respect to time,

                                           ∫ a(t) dt = ∫(t+sin(t)) dt

                                      ⇒ v(t) = $\frac{t^{2} }{2}$ - cos(t) +c

At, t=0, v= -2 so,

                                     ⇒ -2 = 0 - 1 +c

                                     ⇒ c= -1

Hence,

                                     v(t) = $\frac{t^{2} }{2}$ - cos(t) -1

for the velocity to be zero,

                                     0 =  $\frac{t^{2} }{2}$ - cos(t) -1

                                ⇒  t = 1.47 sec (taking only positive value)

So at 1.47 sec the velocity of particle will be zero.