Question

The acceleration of an object (in m/s2) is given by the function a ( t ) = 7 sin ( t ) . The initial velocity of the object is v ( 0 ) = − 10 m/s. Round your answers to four decimal places.

Answer 1

The answer is "
`\bold{v(t) = -7 \cos (t) -3}`"

Step-by-step explanation:

Consider the function
`a(t) = 7 \sin (t)` speed for an Object , and
`V(0) = -10 (m)/(s)` is the initial speed of the object. Find an object-speed v(t) equation:

`\to a(t) = 7 \sin(t) \\\\\to v(t) = \int a(t) dt\\`

`= 7 \int \sin (t) dt \\\\= -7 \cos(t) + C`

Substituting the t = 0 in v(t)

`\to v(0) = - 7 \cos(0) + C \\\\\to -10 = -7(1) +C \\\\\to C = -10 +7\\\\\to C= -3`

after substituting the value C:

`= - 3 in v(t) = -7 \cos (t) +c \\\\\to v(t) = -7 \cos(t) -3`