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t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
Specific impulse (usually abbreviated I sp) is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust. In general, this is a ratio of the impulse, i.e. change in momentum, per mass of propellant. This is equivalent to "thrust per massflow".
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
It is dimensionally equivalent to the momentum unit kilogram-metre per second (kg⋅m/s). One newton-second corresponds to a one-newton force applied for one second. = It can be used to identify the resultant velocity of a mass if a force accelerates the mass for a specific time interval.
Equation [3] involves the average velocity v + v 0 / 2 . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows ...
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
Evaluating these partial derivatives, the former equation becomes =, which reproduces the familiar statement that a body's momentum is the product of its mass and velocity. The time derivative of the momentum is =, which, upon identifying the negative derivative of the potential with the force, is just Newton's second law once again.