Flashcards
Motion in 1D dimension (rectilineo)
Cards in this deck (22)
- 1displacement (vector)Change of position in an time interval.
It is a vector
\[ \Delta x = x_f -x_i\] - 2Average velocity (vector)\[ \bar{v} = \frac{\Delta x}{\Delta t} \]
it is slope of the secant - 3Signs of average velocity+ for \( x_f > x_i\)
- for \( x_f < x_i \) - 4average velocity can be zerowhen the particle ends up at its starting point
- 5Average speed (scalar)says how fast the object is moving
\[ Av. \, speed = \frac{Distancia total}{tiempo total}\] - 6distancia\[ |\Delta x| \]
- 7pitfall prevention Relation between average velocity and average speed?there is not relation
\[ \bar{v} \neq av. \, speed \] - 8Instantaneous velocity (vector) (velocity)it is the slope of the tangent
\[ v = \frac{dv}{dt} = \lim_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t}\] - 9Instantateous speed (scalar) (speed)|v|
- 10Average acceleration (vector)says how the velocity changes as time changes
\[ \bar{a}= \frac{v_f - v_i}{t_f -t_i}\] - 11Instantaneous accelerationa = \frac{dv}{dt}
- 12speeding upwhen vector velocity and acceleration have the same direction
- 13slowing downwhen the vector velocity has opposite direction to the vector acceleration.
- 14Average velocity is numerically equal to the instantaneous velocity ifv is constant, it means that the position of the object changes at the same rate.
In this case \( \bar{v} = v\) - 15Instantaneous acceleration is numerically equal to the average acceleration ifa = cte.
\[ \bar{a} = a\] - 16Equations of motion in 1D constant acceleration\[ v_f = v_0 + a t \]
\[ bar v = \frac{v_f + v_i}{2}\]
\[ x_f = x_i + \frac{1}{2} (v_i + v_f)t \]
\[ x_f = x_i + v_i t + \frac{1}{2}a t^2 \]
\[ v_f^2 = v_i^2 + 2a(x_f - x_i) \] - 17Freely falling objectobject moving freely under the influence of gravity only, regardless of its initial motion.
- 18free fall accelerationany freely object experiences an acceleration directed downwards, regardless its initial motion.
\[ a = -g\] - 19approximation of constant accelerationacceleration due to gravity can decrease with altitude.Therefore, one consider motions near surface Earth and try the acceleration as constant.
- 20uniform motionv = cte
- 21motion uniform accelerationa = cte
- 22motion with no constant accelerationIf \( a \) is known:
\[ v = v_0 + \int_{t_0}^t a dt\]
If a relation between \(x\) and \(a\) is known
\[ \frac{1}{2}v^2 - \frac{1}{2}v_0^2 = \int_{x_0}^{x} a dx\]
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- 1 Motion in one dimension Flashcards on Motion in 1D dimension (rectilineo), created by nquirozp on 11/05/2016.
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