# The velocity of an object with a mass of #3 kg# is given by #v(t)= - t^2 +4 t #. What is the impulse applied to the object at #t= 5 #?

The impulse of an object is associated to a change on its linear momentum,

Let us calculate it for

So impulse finally is given by:

The negative sign just means that the object is moving backwards.

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To find the impulse applied to the object at ( t = 5 ), you need to calculate the change in momentum. Impulse, denoted by ( J ), is equal to the change in momentum, which is the mass times the change in velocity. Therefore, ( J = m \cdot \Delta v ). To find ( \Delta v ) at ( t = 5 ), subtract the initial velocity from the velocity at ( t = 5 ). Given that the initial velocity is ( v(0) = 0 ) (since ( t = 0 )), you can find the velocity at ( t = 5 ) by substituting ( t = 5 ) into the velocity equation ( v(t) = -t^2 + 4t ). Then, calculate ( \Delta v ) and multiply by the mass ( m = 3 ) kg to find the impulse.

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