What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t^{2} - 1$ $a(t) =t^2-1$ from $t \in [2, 3]$ $t in [2, 3]$ ?

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What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t^{2} - 1$ $a(t) =t^2-1$ from $t \in [2, 3]$ $t in [2, 3]$ ?

1 Answer

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Answer 1 · 2016-03-03T04:49:47

$v_{a v g} = \frac{16}{3} m s^{- 1}$ $v_{avg}=16/3ms^-1$

Explanation:

The average of a function can be found by integrating the function over the integral.

So, $v_{a v g} = \int_{2}^{3} a (t) d t = \int_{2}^{3} (t^{2} - 1) d t = (\frac{t^{3}}{3} - t) {∣ ∣ ∣}_{2}^{3}$ $v_{avg}=int_2^3a(t)dt=int_2^3(t^2-1)dt=(t^3/3-t)|_2^3$

Placing the limits, you'll be able to solve and see the answer.

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What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t^{2} - 1$ $a(t) =t^2-1$ from $t \in [2, 3]$ $t in [2, 3]$ ?

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What is the average speed of an object that is still at t=0t=0t=0 and accelerates at a rate of a(t) =t^2-1a(t)=t2−1a(t) =t^2-1 from t in [2, 3]t∈[2,3]t in [2, 3]?

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Explanation:

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What is the average speed of an object that is still at $t = 0$ $t=0$ and accelerates at a rate of $a (t) = t^{2} - 1$ $a(t) =t^2-1$ from $t \in [2, 3]$ $t in [2, 3]$ ?