# The velocity of an object with a mass of #3 kg# is given by #v(t)= sin 8 t + cos 9 t #. What is the impulse applied to the object at #t= ( 7 pi)/ 12 #?

Impulse is defined as change in momentum,

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To find the impulse applied to the object at ( t = \frac{7\pi}{12} ), we need to calculate the change in momentum of the object over a small time interval around ( t = \frac{7\pi}{12} ). Impulse is given by the change in momentum, which can be calculated as the integral of force over time. Given the velocity function ( v(t) = \sin(8t) + \cos(9t) ), the momentum ( p(t) ) of the object at time ( t ) is the integral of ( v(t) ) with respect to ( t ). Therefore, the impulse at ( t = \frac{7\pi}{12} ) is the change in momentum over a small interval around ( t = \frac{7\pi}{12} ).

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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.

- How can an impulse exerted on something be increased?
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- A canoe in a still lake is floating North at #8 m/s#. An object with a mass of #20 kg# is thrown North East at #3 m/s#. If the mass of the canoe was #200 kg # before the object was thrown, what is the new speed and direction of the canoe?
- Why is impulse a vector?
- The kinetic energy of an object with a mass of #2 kg# constantly changes from #32 J# to #84 J# over #4 s#. What is the impulse on the object at #1 s#?

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