The velocity of an object with a mass of $4 k g$ $4 kg$ is given by $v (t) = sin 3 t + cos 6 t$ $v(t)= sin 3 t + cos 6 t$ . What is the impulse applied to the object at $t = \frac{π}{3}$ $t= pi /3$ ?

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Answer 1 · 2018-03-07T01:58:46

The impulse is $- 12$ $-12$ Newton seconds.

We know that impulse is change in momentum. Momentum is given by $p = m v$ $p =mv$ , therefore impulse is given by $J = mDeltav$

So we want to find the rate of change, or the derivative of the velocity function, and evaluate it at time $pi/3$ .

$v'(t) = 3cos(3t) - 6sin(6t)$

$v'(pi/3) = 3cos(3(pi/3)) - 6sin(6(pi/3))$

$v'(pi/3) = -3$

Then we have

$J = mDelta v$

$J= 4(-3)$

$J = -12 kg" "Ns$

Hopefully this helps!

The velocity of an object with a mass of 4 kg4kg4 kg is given by v(t)= sin 3 t + cos 6 t v(t)=sin3t+cos6tv(t)= sin 3 t + cos 6 t . What is the impulse applied to the object at t= pi /3 t=π3t= pi /3 ?