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11 months, 1 week ago

# Help me understand! If Force F= 500- 100t, then impulse as a function of time will be:

If Force F= 500- 100t, then impulse as a function of time will be:

• Option 1)

$500t - 50 t^{2}$

• Option 2)

$50t-10$

• Option 3)

$50 - t^{2}$

• Option 4)

$-\alpha v^{2}$

571 Views
P Plabita
Answered 11 months, 1 week ago

As discussed in

Impulse Momentum Theorem -

$\vec{F}=\frac{d\vec{p}}{dt}$

$\int_{t_{1}}^{t_{2}}\vec{F}dt=\int_{p_{1}}^{p_{2}}\vec{dp}$

- wherein

If $\bigtriangleup t$  is increased, average force is decreased

$f = 500-100d$

$dp = f\cdot dt = \int_{P_{i}}^{P_{t}}dP= \int (500-100d)dt$

$P_{t}-P_{i} = 500t - 100\frac{p^{2}}{2}$

$\Delta P=I$ (Change in linear Momentum = Impulse)

$\therefore I=500t-500t^{2}$

Option 1)

$500t - 50 t^{2}$

This solution is correct.

Option 2)

$50t-10$

This solution is incorrect.

Option 3)

$50 - t^{2}$

This solution is incorrect.

Option 4)

$-\alpha v^{2}$

This solution is incorrect.

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