The velocity of an object with a mass of #6 kg# is given by #v(t)= te^t-e^t #. What is the impulse applied to the object at #t= 3 #?

Answer 1

Impact cannot defined for an instant of time. Impact is defined for an interval of time. So the answer for this question is zero.

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Answer 2

Charles Aeschliman

To find the impulse applied to the object at ( t = 3 ), you need to calculate the change in momentum of the object over a small interval around ( t = 3 ). Impulse is defined as the change in momentum.

Calculate the momentum of the object at ( t = 3 ) using the velocity function ( v(t) = t e^t - e^t ).
Calculate the momentum of the object at ( t = 3 - \delta t ) (just before ( t = 3 )) using the velocity function.
Calculate the change in momentum by subtracting the momentum at ( t = 3 - \delta t ) from the momentum at ( t = 3 ).
The impulse is equal to the change in momentum.

After calculating the impulse, you will have the answer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.