The velocity of an object with a mass of $8 k g$ $8 kg$ is given by $v (t) = sin 4 t + cos 13 t$ $v(t)= sin 4 t+ cos 13 t$ . What is the impulse applied to the object at $t = \frac{3 π}{4}$ $t= ( 3 pi)/ 4$ ?

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The velocity of an object with a mass of $8 k g$ $8 kg$ is given by $v (t) = sin 4 t + cos 13 t$ $v(t)= sin 4 t+ cos 13 t$ . What is the impulse applied to the object at $t = \frac{3 π}{4}$ $t= ( 3 pi)/ 4$ ?

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Answer 1 · 2016-02-09T15:54:48

$¯ ¯ ¯ J = 5, 656 N.s$ $bar J=5,656 " N.s"$

Explanation:

$¯ ¯ ¯ J = \int F (t) \cdot d t$ $bar J=int F(t)*d t$
$F = m \cdot a = m \cdot \frac{d v}{d t}$ $F=m*a=m*(d v)/(d t)$
$¯ ¯ ¯ J = \int m \cdot \frac{d v}{d t} \cdot d t$ $bar J=int m*(d v)/(d t)*d t$
$¯ ¯ ¯ J = m \int d v$ $bar J=m int d v$
$d v = (4 cos 4 t - 13 sin 13 t) \cdot d t$ $d v=(4cos4t -13sin13t)*d t$
$¯ ¯ ¯ J = m \int (4 cos 4 t - 13 sin 13 t) \cdot d t$ $bar J=m int (4cos4t-13sin13t)*d t$
$¯ ¯ ¯ J = m (sin 4 t + cos 13 t)$ $bar J=m(sin4t+cos13t)$
$¯ ¯ ¯ J = 8 (sin 4 \cdot 3 \frac{π}{4} + cos 13 \cdot 3 \frac{π}{4})$ $bar J=8(sin4*3pi/4+cos13*3pi/4)$
$¯ ¯ ¯ J = 8 \cdot (0 + 0, 707)$ $bar J=8*(0+0,707)$
$¯ ¯ ¯ J = 8 \cdot 0, 707$ $bar J=8*0,707$
$¯ ¯ ¯ J = 5, 656 N.s$ $bar J=5,656 " N.s"$

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The velocity of an object with a mass of $8 k g$ $8 kg$ is given by $v (t) = sin 4 t + cos 13 t$ $v(t)= sin 4 t+ cos 13 t$ . What is the impulse applied to the object at $t = \frac{3 π}{4}$ $t= ( 3 pi)/ 4$ ?

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Science

Math

Humanities

... and beyond

The velocity of an object with a mass of 8kg8 kg is given by v(t)=sin4t+cos13tv(t)= sin 4 t+ cos 13 t . What is the impulse applied to the object at t=3π4t= ( 3 pi)/ 4 ?

1 Answer

Explanation:

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The velocity of an object with a mass of $8 k g$ $8 kg$ is given by $v (t) = sin 4 t + cos 13 t$ $v(t)= sin 4 t+ cos 13 t$ . What is the impulse applied to the object at $t = \frac{3 π}{4}$ $t= ( 3 pi)/ 4$ ?