Aparticle moves on a line away from its initial position so that after t hours it is s = 2t^2 +3t miles from its initial position. find the average velocity of the particle over the interval [1, 4]. include units in your answer.

Average speed of the particle is 13 miles per hour.

Step-by-step explanation:

From the given question expression for distance traveled by the particle is

Then fro the time interval (1, 4) we have to calculate the average speed.

At t=1, s=2(1)²+3(1) =2+3 =5 miles

And at t = 4 s=2(4)²+3(4) = 2(16)+12 = 32+12 =44 miles

So displacement of the particle in the time span from 1 to hours.

s = (44-5) = 39 miles

And the times taken = (4-1) =3 hours

From the formula speed = displacement/(time taken for displacement)

V = 39/3 = 13 miles/hour

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step-by-step explanation: