Question

The acceleration of an object (in m/s2) is given by the function a ( t ) = 6 sin ( t ) a(t)=6sin(t). The initial velocity of the object is v ( 0 ) = − 2 v(0)=-2 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity.

Answer 1

Answer:

$v(t)=-6cos(t)+4$

Explanation:

We have acceleration given by

$a(t)=6sin(t)$

Velocity at t = 0

$v(0)=-2\ m/s$

Velocity is given by

$v(t)=\int a(t)dt\\\Rightarrow v(t)=\int 6sin(t)dt\\\Rightarrow v(t)=6\int sin(t)\\\Rightarrow v(t)=-6cost+C$

at t = 0

$-2=-6cos0+C\\\Rightarrow -2+6=C\\\Rightarrow C=4$

The equation will be

$\mathbf{v(t)=-6cos(t)+4}$

Answer 2

Answer:

v(t) = - 6 cos t + 4

Explanation:

The acceleration function is given by

a(t) = 6 Sin t

Acceleration is defined as the time derivative of velocity, so integrate on both the sides, we get

v = - 6 Cos t + c     .... (1)

put, t = 0 then v = -2 m/s

- 2 = - 6 + c

c = 4

Put in equation (1), we get

v = - 6 Cos t + 4

Thus, the equation of the function of velocity is v(t) = - 6 cos t + 4.