Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4. (4 points)

A.) v(t) = t2 + cos(t) + 3

B.) v(t) = 2 + cos(t) + 1

C.) v(t) = t2 - cos(t) + 5

D.) v(t) = t2 + sin(t) + 4

Please Help! I think the answer is D

The answer is (c) v(t) = t² - cos(t) + 5

Step-by-step explanation:

Given the acceleration a(t) = 2t + sin(t), we can calculate the velocity. Acceleration(a) is the time rate of velocity(v), it is the differential of velocity with respect to time(t) and is given by the equation:

cross multiplying, we get

Therefore

To calculate v(t) we integrate both sides

therefore , but a(t) = 2t + sin(t)

to get c At t = 0, v(0) = 4

substituting c = 5 we get

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2