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

answer is : muchas/tipicas

have a nice day!

~recklesschicken

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.