Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
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 …
As used in this context it is not the same as the physical change in velocity of the vehicle. Delta-v is produced by reaction engines such as rocket engines and is proportional to the thrust per unit mass and burn time and is used to determine the mass of propellant required for the given manoeuvre through the rocket equation .
The velocity of an object is the rate of change of its position with respect to a frame of reference and is a function of time . Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north). Velocity is a fundamental concept in kinematics the branch of classical mechanics that describes the motion of bodies.
Constant acceleration allows for the velocity vs. time graph to appear as straight lines thus designating a relationship between displacement (ΔR) maximum velocity (v peak) acceleration (a) and time(Δt). The following equations show this. ΔR = 1 / 2 v peak Δt ΔR = 1 / 4 a(Δt) 2. Given the displacement and time both the maximum velocity and acceleration of each mechanism in a given pair can be calculated.
Tsiolkovsky rocket equation - Wikipedia
As a vector jerk j can be expressed as the first time derivative of acceleration second time derivative of velocity and third time derivative of position: j ( t ) = d a ( t ) d t = d 2 v ( t ) d t 2 = d 3 r ( t ) d t 3 {\displaystyle \mathbf {j} (t)={\frac {\mathrm {d} \mathbf {a} (t)}{\mathrm {d} t}}={\frac {\mat...
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