Mathematics, 01.03.2020 11:49 emzaa

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?

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Answer from: Masonb5993

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: link

Answer from: chyg304

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 from: Quest

the correct answer is 5

Answer from: Quest

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