SOLUTION: when a body is being uniformly accelerated, the distance, D travelled is the sum of two parts: one part varies as the time t, the other varies as the square of time. the distance t

Question 1201364: when a body is being uniformly accelerated, the distance, D travelled is the sum of two parts: one part varies as the time t, the other varies as the square of time. the distance travelled by a body in 2 seconds and 3 seconds from its original position are respectively 32m and 57m. find (a) the formular connecting d and t (b) d when t= 4s
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The general form of the distance vs. time formula is:
D(t) = a*t + b*t^2
Given: D(2) = 32 and D(3) = 57
Thus, we have 2 equations and 2 unknowns, a and b:
32 = 2a + 4b (1)
57 = 3a + 9b (2)
Solving for a in (1) gives a = 16 - 2b
Inserting in (2) gives 57 = 3(16-2b) + 9b -> b = 3
32 = 2a + 4(3) -> a = 10
Ans: D(t) = 10t + 3t^2

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