The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = t^{3} + 3 t^{2}$ $v(t)= t^3 + 3 t^2$ . What is the impulse applied to the object at $t = 4$ $t= 4$ ?

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The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = t^{3} + 3 t^{2}$ $v(t)= t^3 + 3 t^2$ . What is the impulse applied to the object at $t = 4$ $t= 4$ ?

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Answer 1 · 2016-02-26T22:07:56

$I (4) = 2 (4 \cdot 4^{2} + 3 \cdot 4^{2}) = 7 \cdot 4^{2} = 112 N s$ $I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s$
Careful however Impulse is not $m v (t)$ $mv(t)$ evaluate at $t = 4 s$ $t = 4 s$
it is Force applied for a finite amount of time $F*Deltat$
in the limit $I = int_(t_1)^(t_(2))Fdt$

Explanation:

This is a straight implementation of the impulse equation i.e.
$F = m(dv)/dt$ Newton law ==> (1)
$I = F dt = m(dv)$ Impulse equation ==> (2)
While the question is not clear I will make the assumption the Force was applied for 4 seconds causing the change in speed from
$v(0) = 0 -> v(4)$ and $I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s$

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The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = t^{3} + 3 t^{2}$ $v(t)= t^3 + 3 t^2$ . What is the impulse applied to the object at $t = 4$ $t= 4$ ?

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The velocity of an object with a mass of 2 kg2kg2 kg is given by v(t)= t^3 + 3 t^2 v(t)=t3+3t2v(t)= t^3 + 3 t^2 . What is the impulse applied to the object at t= 4 t=4t= 4 ?

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Explanation:

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The velocity of an object with a mass of $2 k g$ $2 kg$ is given by $v (t) = t^{3} + 3 t^{2}$ $v(t)= t^3 + 3 t^2$ . What is the impulse applied to the object at $t = 4$ $t= 4$ ?