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An automobile accelerates from rest at 1 + 3√t mph/sec for 9 seconds.

(a) What is its velocity after 9 seconds?

User Augustzf
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1 Answer

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Final answer:

The velocity of the car after 9 seconds is 12.6 mph.

Step-by-step explanation:

To find the velocity of the car after 9 seconds, we need to integrate the acceleration function from 0 to 9. The acceleration function is given as a(t) = 1 + 3√t mph/sec. To integrate this function, we can use the power rule of integration.

The integral of a(t) with respect to t is ∫(1 + 3√t) dt = t + 6√t/5 + C, where C is the constant of integration. Evaluating this integral from 0 to 9 gives us ∫(0 to 9) a(t) dt = (9 + 6√9/5) - (0 + 6√0/5) = 9 + 18/5 = 9 + 3.6 = 12.6 mph.

Therefore, the velocity of the car after 9 seconds is 12.6 mph.

User T Davey
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