Question

The formula a=−66t deseribes a, the acceleration of an object in inches/second, In terms of, t, the elapsed time in seconds. If the object moves a distance of 2736 inches in the first 4 seconds, find its initial velocity.

Answer 1

To find the initial velocity, integrate the acceleration function and solve for the constant of integration using the given information of the distance traveled in the first 4 seconds.

Step-by-step explanation:

To find the initial velocity of an object, we can integrate the acceleration function. Given the equation a = -66t, we need to integrate it with respect to t to find v, the velocity function.

Integrating -66t gives us v = -33t^2 + C, where C is the constant of integration.

We can then use the given information of the distance traveled in the first 4 seconds to find the value of C.

Since the object moves a distance of 2736 inches in the first 4 seconds, we can set up the following equation:

2736 inches = -33(4)^2 + C

Solving for C, we get C = 2736 + 33(4)^2 = 2736 + 528 = 3264.

Substituting the value of C back into the velocity function, we have v = -33t^2 + 3264.

Therefore, the initial velocity of the object is 3264 inches/second.

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