contestada

The acceleration function a(t) (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.
a(t)=2t+4,

v(0)=-5

(a) Find the velocity v(t) at time t.

v(t)= ? m/s

(b) Find the total distance d traveled during the time interval given above.

d=? m

Respuesta :

wyskoj

Answer:

A: [tex]v(t)=-t^2+4t-5[/tex]

Step-by-step explanation:

Acceleration is second derivative of position, velocity is first derivative. Therefore, the velocity is the integral of acceleration.

[tex]v(t)=\int\ {2t+4} \, dt[/tex]

Integrate:

[tex]-t^2+4t+C[/tex]

V(0)=-5:

[tex]-0^2+4(0)+C=-5\\C=-5[/tex]

Therefore, v(t):

[tex]v(t)=-t^2+4t-5[/tex]

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