What is the direction of instantaneous acceleration?
What is the direction of instantaneous acceleration?
- In simple terms if velocity is increasing in any particular direction at any instant, then the acceleration has a positive component in the direction of velocity at the same instant.
Take the velocity vector a two points separated by an infinitesimally small time interval. Subtract the later vector from the earlier, and divide by the infinitesimally small time interval. The resulting vector is the instantaneous acceleration (in the limit that the time interval goes to zero). The direction of that vector is the direction of the acceleration.
In finding velocity graphically, we plot the xxcomponent of the position vector and the yycomponent of position vector for each instant of time. We end up with a curve: the trajectory. The direction of the velocity is tangent to the curve at each point of time. The analog of that method to find the direction of acceleration is to plot vyvy and vxvx for each instant of time on graph paper. The direction of acceleration is tangent to that curve at each point of time.
You can't find the direction of acceleration directly from the trajectory, although if you had some extra information, namely the value of time at each point on the trajectory, you could figure it out with some work.
- In simple terms if velocity is increasing in any particular direction at any instant, then the acceleration has a positive component in the direction of velocity at the same instant.
Take the velocity vector a two points separated by an infinitesimally small time interval. Subtract the later vector from the earlier, and divide by the infinitesimally small time interval. The resulting vector is the instantaneous acceleration (in the limit that the time interval goes to zero). The direction of that vector is the direction of the acceleration.
In finding velocity graphically, we plot the xxcomponent of the position vector and the yycomponent of position vector for each instant of time. We end up with a curve: the trajectory. The direction of the velocity is tangent to the curve at each point of time. The analog of that method to find the direction of acceleration is to plot vyvy and vxvx for each instant of time on graph paper. The direction of acceleration is tangent to that curve at each point of time.
You can't find the direction of acceleration directly from the trajectory, although if you had some extra information, namely the value of time at each point on the trajectory, you could figure it out with some work.
