Impulse Imparted by Constant Force

Theorem

Let a constant force $\mathbf F$ be applied to a particle $P$ from time $t_1$ to time $t_2$.

Then the impulse $\mathbf J$ imparted to $P$ is:

$\mathbf J = \mathbf F \paren {t_2 - t_1}$

Proof

\(\ds \mathbf J\)

\(=\)

\(\ds \int_{t_1}^{t_2} \mathbf F \rd t\)

Definition of Impulse

\(\ds \)

\(=\)

\(\ds \bigintlimits {\mathbf F t} {t \mathop = t_1} {t \mathop = t_2}\)

Definite Integral of Constant

\(\ds \)

\(=\)

\(\ds \mathbf F \paren {t_2 - t_1}\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): impulse: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): impulse: 1.