The position of a particle moving along a line is given by s(t) = 2t3 - 24t2 + 90t + 7 for t ≥ 0. for what values of t is the speed of the particle increasing?

The speed of the particle increases for

Step-by-step explanation:

Given:

To find the speed of the particle, we need a second derivative of the equation

Differentiating, we get,

Again differentiating , we get,

Since, we need to find at what value the speed of the particle increasing, we need to equate to find the interval at which the speed of the particle increases. Thus,

Thus, the interval are and

Substituting any one value between the interval in the equation

The speed of the particle does not increase at the interval

Now, substituting any one value between the interval in the equation

Thus, the speed of the particle increases during the interval

Hence, the speed of the particle increases for

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