Answer:
(a)
(b)
(c) The position of the particle is
(d) The position of the particle is
Step-by-step explanation:
An anti-derivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x) = f(x), then F(x) is an anti-derivative of f(x).
If F(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted,
, c is any constant.
(a) To find f(t) of you must:
1.
2.
3.
(b) To find f(x) of you must:
1.
We use f''(0) = 6 to find the value of C
Thus,
2.
We use f'(0) = 6 to find the value of D
Thus,
3.
We use f(0) = 7 to find the value of E
Thus,
(c) You need to use the relation to find the position of the particle.
We know that , so
We use s(0) = 3 to find the value of C
Therefore, the position of the particle is
(d) You need to use the relation to find the velocity of the particle.
We know that , so
Next, you need to use the relation to find the position of the particle.
We know that , so
We use s(0) = 0, s(1) = 20 to find the value of C and D
Therefore, the position of the particle is