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Cato11

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- TL;DR Summary
- How to achieve non-uniform acceleration?

Hello everyone, I would really appreciate some help with a challenge I am facing. The challenge is to accelerate a particle in a circular path, but the acceleration must be non-uniform. In other words, the velocity does not increase linearly. The problem I am facing is shown below:

1. The particle starts at the Start Position (in this case 0°) with a speed of 120°/s.

2. The particle must accelerate to the End Position (in this case 180° away) where it has a speed of 240°/s

3. The acceleration must follow the profile in the graph, i.e. it must accelerate rapidly at the start after which the rate should decrease

- Does anyone know how I can find the time (t) it takes to undergo this acceleration? It must occur precisely within the 180° of displacement.

I am writing a computer program to animate this motion. I can quite easily alter the particle's speed to follow the curve, but I need to know the timescale within which to do this. As a side note, I have been able to achieve uniform acceleration in this scenario using the rotational versions of the linear motion equations, but I believe that these no longer apply in the case of non-uniform acceleration. Please correct me if I am wrong though.

Any help would be appreciated tremendously!

**The scenario:**1. The particle starts at the Start Position (in this case 0°) with a speed of 120°/s.

2. The particle must accelerate to the End Position (in this case 180° away) where it has a speed of 240°/s

3. The acceleration must follow the profile in the graph, i.e. it must accelerate rapidly at the start after which the rate should decrease

**The problem:**- Does anyone know how I can find the time (t) it takes to undergo this acceleration? It must occur precisely within the 180° of displacement.

**The context:**I am writing a computer program to animate this motion. I can quite easily alter the particle's speed to follow the curve, but I need to know the timescale within which to do this. As a side note, I have been able to achieve uniform acceleration in this scenario using the rotational versions of the linear motion equations, but I believe that these no longer apply in the case of non-uniform acceleration. Please correct me if I am wrong though.

Any help would be appreciated tremendously!