Question

Answer only if u know
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Answer 1

Given :

Mass of body = 3 kg

Position Vector (r) = (3t)i - (4cos t) j m

Differentiating the position vector (r) w.r.t 't' in order to get velocity.

V = dr/dt

V = 3i + 4 sint j

Again, Differentiating 'V' w.r.t 't' in order to get acceleration.

a = dv/dt

a = d(3i + 4sint j)/dt

a = 4cost j

For impulse we need to find force.

Force = ma

F = 3 × 4cost j

F = 12 cost j

Now, we are required to find impulse using integration.

$I = \int{Fdt}$

$I = \int ^{ \binom{\pi}{2} } _{0} \: 12 cost \: dt \: j$

$I = \int ^{ \binom{\pi}{2} } _{0} \: 12 sint \: j$

$I = 12 [Sint]^{ \frac{\pi}{2} } _{0}$

$I = </strong><strong>(</strong><strong>12\: </strong><strong>N-s</strong><strong>)</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>j</strong><strong>$

Therefore, the impulse = I = (12 N-s) j

Answer 2

Answer:-

• Mass ⇒ 3Kg
• Position Vector ⇒ (3tî - 4cos t j ) m

Let us differentiate the position vector with respect to time to get velocity.

$\implies\:v\:=\:\frac{dr}{dt} \implies\:v\:=\:3i\:+4sin\:t\:j$

Let us differentiate the velocity with respect to time to get acceleration.

$\implies\:a\:=\:\frac{dv}{dt}\: \implies\:a\:=\:\frac{d(\:3i\:+\:4sin\:t\:j)}{dt} \implies\:a\:=\:4cos\:t\:j$

To calculate the impulse it is necessary to find the force

• By Newton's Second law of motion we know that,
• F = m a
• F = 3 × 4cos t j
• F = 12cos t j

Therefore we have the force calculated

Now, we can find the impulse,

I = ∫Fdt

$I \:=∫^_0(\frac{\pi}{2})\:\implies\:I\: =\:12[Sin\:t]^\frac{\pi}{2} _0$

$\mapsto \sf\boxed{\bold{\pink{\implies\:I\: =\:12[Sin\:t]^\frac{\pi}{2} _0\:}}}$

Thanks

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