The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = sin 5 t + cos 6 t$ $v(t)= sin 5 t + cos 6 t$ . What is the impulse applied to the object at $t = \frac{π}{4}$ $t= pi /4$ ?

Question

The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = sin 5 t + cos 6 t$ $v(t)= sin 5 t + cos 6 t$ . What is the impulse applied to the object at $t = \frac{π}{4}$ $t= pi /4$ ?

1 Answer

Impact of this question

1678 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-05T14:13:52

$\int F d t = - 1, 414212 N.s$ $int F d t=-1,414212 " N.s"$

Explanation:

$J = \int F . d t'impulse'$ $J=int F.d t " 'impulse'"$
$M = \int m . d v'momentum'$ $M=int m.d v " 'momentum'"$
$\int F . d t = \int m . d v$ $int F. d t=int m. d v$
$v (t) = sin 5 t + cos 6 t$ $v(t)=sin5t + cos6t$
$d v = (5 . cos 5 t - 6 . sin 6 t) d t$ $d v= (5 .cos5 t-6.sin6t)d t$
$\int F . d t = m \int (5 . cos 5 t - 6 . sin 6 t) d t$ $int F.d t=m int (5. cos5t- 6. sin6t) d t$
$\int F d t = 2 (5 \int cos 5 t d t - 6 \int sin 6 t d t)$ $int F d t=2 (5 int cos5t d t- 6 int sin6t d t)$
$\int F d t = 2 (\frac{5.1}{5} . sin 5 t + \frac{6.1}{6} cos 6 t)$ $int F d t=2(5.1/5 .sin5t+ 6.1/6 cos 6t)$
$\int F d t = 2 (sin 5 t + cos 6 t)$ $int F d t=2(sin 5t + cos 6t)$
$for t= \frac{π}{4}$ $"for t="pi/4$
$\int F d t = 2 (sin 5 \frac{π}{4} + cos 6 \frac{π}{4})$ $int F d t=2(sin 5pi/4 + cos6pi/4)$
$\int F d t = 2 (- 0, 707106 + 0)$ $int F d t=2(-0,707106+0)$
$\int F d t = - 1, 414212 N.s$ $int F d t=-1,414212 " N.s"$

Science

Math

Humanities

... and beyond

The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = sin 5 t + cos 6 t$ $v(t)= sin 5 t + cos 6 t$ . What is the impulse applied to the object at $t = \frac{π}{4}$ $t= pi /4$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

The velocity of an object with a mass of 2kg2 kg is given by v(t)=sin5t+cos6tv(t)= sin 5 t + cos 6 t . What is the impulse applied to the object at t=π4t= pi /4 ?

1 Answer

Explanation:

Related questions

Impact of this question

The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = sin 5 t + cos 6 t$ $v(t)= sin 5 t + cos 6 t$ . What is the impulse applied to the object at $t = \frac{π}{4}$ $t= pi /4$ ?