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

hi,

6x times 4 is 24x and 5 times 4 is 20, so the answer is 24x+20.

hope this and for a little humor i am groot.

Iknow it’s simple i guess but can someone solve it for me.

Answer from: Quest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

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At time t>=0, the acceleration of a particle moving on the x-axis is a(t)=t+sin(t). At t=0, the v...

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