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

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208