The velocity of an object with a mass of #2 kg# is given by #v(t)= t^3 + 3 t^2 #. What is the impulse applied to the object at #t= 4 #?
Careful however Impulse is not
it is Force applied for a finite amount of time
in the limit
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To find the impulse applied to the object at ( t = 4 ), you need to calculate the change in momentum. Impulse is defined as the change in momentum, which can be found by integrating the force over the time interval. In this case, impulse ( J ) can be calculated using the formula:
[ J = \int_{t_1}^{t_2} F(t) , dt ]
Given that velocity ( v(t) = t^3 + 3t^2 ), the force ( F(t) ) can be found by taking the derivative of velocity with respect to time, ( F(t) = \frac{dv}{dt} ). Then, calculate the impulse ( J ) by integrating the force from ( t = 0 ) to ( t = 4 ):
[ J = \int_{0}^{4} F(t) , dt ]
After integrating, you'll have the impulse applied to the object at ( t = 4 ).
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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.
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.
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.
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.
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