# [Answer] Impulse is a vector or scalar?

Impulse is a vector or scalar?

Velocity – Wikipedia

Velocity – Wikipedia

Impulse vector – Wikipedia

Delta-v (physics) – Wikipedia

In classical mechanics impulse (symbolized by J or Imp) is the integral of a force F over the time interval t for which it acts. Since force is a vector quantity impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector …

For a vibratory second-order system $\omega _{n}^{2}/(s^{2}+2\zeta \omega _{n}+\omega _{n}^{2})$ with undamped natural frequency $\omega _{n}$ and damping ratio $\zeta$ the magnitude $I_{i}$ and angle $\theta _{i}$ of an impulse vector $\mathbf {I} _{i}$ corresponding to an impulse function $A_{i}\delta (t-t_{i})$ $i=1 2 … n$ is defined in a 2-dimensional polar coordinate system as

For a vibratory second-order system $\omega _{n}^{2}/(s^{2}+2\zeta \omega _{n}+\omega _{n}^{2})$ with undamped natural frequency $\omega _{n}$ and damping ratio $\zeta$ the magnitude $I_{i}$ and angle $\theta _{i}$ of an impulse vector $\mathbf {I} _{i}$ corresponding to an impulse function $A_{i}\delta (t-t_{i})$ $i=1 2 … n$ is defined in a 2-dimensional polar coordinate system as $I_{i}=A_{i}e^{\zeta \omega _{n}t_{i}}$ $\theta _{i}=\omega _{d}t_{i}$ where $A_{i}$ implies the magnitude of an impulse function $t_{i}$ implies the time location of the impulse function and $\omega _{d}$ implies damped natural frequency $\omega _{n}{\sqrt {1-\zeta ^{2}}}$. For a positive impulse function with $A_{i}>0$ the initial point of the impulse vector is located at the origin of the polar coordinate system while for a negative impulse function with $A_{i}<0$ the terminal point of the impulse vector is located at the origin. □ In this definition the magnitude $I_{i}$ is the product of $A_{i}$ and a scaling factor for damping during time interval $t_{i}$ which represents the magnitude $A_{i}$ before being damped; the angle $\theta _{i}$ is the product of the impulse time and damped natural frequency. $\delta (t-t_{i})$ represents the Dirac delta function with impulse time at $t=t_{i}$. Note that an impulse function is a purely mathematical quantity while the impulse vector includes a physical quantity (that is $\omega _{n}$ and $\zeta$of a second-order system) as well as a mathematical impul… The scalar absolute value of velocity is called speed being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s −1). For example "5 metres per second" is a scalar whereas "5 metres per second east" is a vector . ...