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.

Answer 2

The value of t when the velocity of the particle is zero is approximately 1.47s.

Acceleration function

Given the particle acceleration modeled by the function expressed as:

• a(t)=t+sin(t)

To get the velocity, we will have to integrate the function as shown:

• $v(t)=\int\limits {(t+sint)} \, dt \\v(t)=t^2/2 -cost + C$

If at t=0, the velocity of the particle is -2, then;

$-1 = 0-cos(0) + C\\-1 = 0-1 + C\\C = 0$

The velocity function will become:

$v(t)=t^2/2-cost$

The value of t when the velocity is zero is expressed as:

$0 =t^2/2 -cos(t)-1\\t \approx 1.47s$

Hence the value of t when the velocity of the particle is zero is approximately 1.47s.

Learn more on velocity function here: https://brainly.com/question/25749514