Respuesta :

Answer:

Given equation of motion of a particle is,

[tex]s(t)=4t^3+36t^2+96t[/tex]

To find the velocity function of t, value of t when the velocity is zero and acceleration of the particle.

Explanation:

we know that, velocity of a particle is rate of change of the object’s position with respect to a frame of reference and time.

we get,

[tex]v(t)=\frac{d}{dt}(s(t))[/tex]

Substitute for s(t), we get

[tex]v(t)=\frac{d}{dt}(4t^3+36t^2+96t)[/tex]

Differenting we get,

[tex]v(t)=12t^2+72t+96[/tex]

Required velocity function is,

[tex]v(t)=12t^2+72t+96[/tex]

when velocity equal to 0, we get

[tex]12t^2+72t+96=0[/tex]

Dividing by 12, we get

[tex]t^2+6t+8=0[/tex]

we get,

[tex]t^2+4t+2t+8=0[/tex][tex]t(t+4)+2(t+4)=0[/tex]

Taking (t+4) as common we get,

[tex](t+4)(t+2)=0[/tex]

we get,

[tex]t=-4,-2[/tex]

The values of t are,

t=-4 and t=-2

To find acceleration of a particle.

we know that,

Acceleration a(t) is the rate at which velocity (speed) is changing.

we get,

[tex]a(t)=\frac{d}{dt}(v(t))[/tex]

Substitute v(t), we get,

[tex]a(t)=\frac{d}{dt}(12t^2+72t+96)[/tex]

we get,

[tex]a(t)=24t+72[/tex]

The acceleration of a particle is,

[tex]a(t)=24t+72[/tex]

ACCESS MORE
EDU ACCESS