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

For a vibratory second-order system ${\displaystyle \omega _{n}^{2}/(s^{2}+2\zeta \omega _{n}+\omega _{n}^{2})}$ with undamped natural frequency ${\displaystyle \omega _{n}}$ and damping ratio ${\displaystyle \zeta }$ the magnitude ${\displaystyle I_{i}}$ and angle ${\displaystyle \theta _{i}}$ of an impulse vector ${\displaystyle \mathbf {I} _{i}}$ corresponding to an impulse function ${\displaystyle A_{i}\delta (t-t_{i})}$ ${\displaystyle i=1 2 … n}$ is defined in a 2-dimensional polar coordinate system as ${\displaystyle I_{i}=A_{i}e^{\zeta \omega _{n}t_{i}}}$ ${\displaystyle \theta _{i}=\omega _{d}t_{i}}$ where ${\displaystyle A_{i}}$ implies the magnitude of an impulse function ${\displaystyle t_{i}}$ implies the time location of the impulse function and ${\displaystyle \omega _{d}}$ implies damped natural frequency ${\displaystyle \omega _{n}{\sqrt {1-\zeta ^{2}}}}$. For a positive impulse function with ${\displaystyle A_{i}>0}$ the initial point of the impulse vector is located at the origin of the polar coordinate system while for a negative impulse function with ${\displaystyle A_{i}<0}$ the terminal point of the impulse vector is located at the origin. □ In this definition the magnitude ${\displaystyle I_{i}}$ is the product of ${\displaystyle A_{i}}$ and a scaling factor for damping during time interval ${\displaystyle t_{i}}$ which represents the magnitude ${\displaystyle A_{i}}$ before being damped; the angle ${\displaystyle \theta _{i}}$ is the product of the impulse time and damped natural frequency. ${\displaystyle \delta (t-t_{i})}$ represents the Dirac delta function with impulse time at ${\displaystyle t=t_{i}}$. Note that an impulse function is a purely mathematical quantity while the impulse vector includes a physical quantity (that is ${\displaystyle \omega _{n}}$ and ${\displaystyle \zeta }$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 . ...