The object starts to move in a straight line with an initial velocity of 5. Given that the acceleration at any time t is the square of T plus 2 times T, please express the displacement s as a function of time t Function problem

According to the meaning of the problem, the acceleration of the object a = (T ^ 2 + 2) * t, in order to find out the functional relationship between displacement s and time t, we must use the knowledge of higher numbers. I don't know if you have learned? A = DV / dt = (T ^ 2 + 2) t = T ^ 3 + 2T so, v = ∫ (T ^ 3 + 2t) DT = 1 / 4 * T ^ 4 + T ^ 2 + C (C represents any constant) the initial velocity of the object VO = 5m / s, so when t = 0

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1. It is proved that: (1) if the difference of displacement of an object moving uniformly in a straight line is a fixed value in any two continuous equal time, and the acceleration is a, the continuous equal time is t, and the difference of displacement is △ x, then △ x = at2. (2) in the uniformly variable linear motion, the instantaneous velocity at the midpoint of displacement is VX2 = V20 + v2t2
2. It is proved that the displacement difference of an object moving in a straight line with uniform speed change in any two consecutive equal times is a fixed value
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5. The results are as follows: 1. The spring oscillator moves harmoniously, the velocity at T1 is V, the velocity at T2 is V, and the direction is the same. Given that (t2-t1) is less than the period T, then (t2-t1) The results are as follows: 1. When the spring oscillator moves harmoniously, the velocity is V at T1 and V at T2, and the direction is the same. It is known that (t2-t1) is less than period T, then (t2-t1) () A. May be greater than a quarter of a cycle B. may be less than a quarter of a cycle C. It must be less than half period D. it may be equal to half period D Why don't you choose D?
6. The velocity of the spring oscillator is V at T1 and V at T2, and the direction is the same. It is known that (t2-t1) is less than the period T, then (t2-t1) () A. May be greater than a quarter of a cycle B. may be less than a quarter of a cycle C. must be less than a half of a cycle D. may be equal to a half of a cycle
7. If the length of the spring is the same at T1 and T2, then it is certain that the oscillator will vibrate at these two moments () A. Equal displacement and opposite direction B. equal velocity and same direction C. equal acceleration and same direction D. equal velocity and opposite direction
8. If t2-t1 = t / 4, then the distance between two points AB may be a.0 B. equal to a C. greater than a D. less than a
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