An object's acceleration is given by a (t) = a (t) = 60t m/s260t m/s2. if it begins at rest, how far has it gone after 10 seconds?

Question

Skyler Carlson

Physics

1 January, 04:51

An object's acceleration is given by a (t) = a (t) = 60t m/s260t m/s2. if it begins at rest, how far has it gone after 10 seconds?

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Camren Fox · Answer 1

The object's acceleration is given by the expression: a (t) = 60t m/s^2. The distance it traveled after 10 seconds after starting from rest can be obtained by integrating the expression, a (t), twice in order to get the expression for the distance as a function of time.

The first integral of a (t) is the velocity, v (t), of the object which is then equal to: v (t) = 30t^2. The integral of v (t) is then distance, d (t), of the object which is then equal to: d (t) = 10t^3. With the distance equation available, we simply plug in t = 10 seconds into the equation. It is then determined that the object has traveled 10,000 m or 10 km after 10 seconds starting from rest.