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I came across a question in which a body had both tangential and normal acceleration. I attempted to find out distance travelled by the body in a particular time period as per the question demanded. However the solution stated that the distance travelled was only dependent on the tangential acceleration and not on the normal acceleration. So I wonder is the trajectory a conic and that's the reason why normal acceleration doesn't come into play while calculating the distance?

(I don't have the greatest idea about conics so I guessed the fact that distance travelled by a particle in a conic trajectory is independent of normal acceleration)

crimsonKnight
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1 Answers1

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The distance travelled can be given by $\int|\frac{dr}{dt}|dt$. The normal acceleration doesn't change the absolute velocity $|\frac{dr}{dt}|$. So the distance travelled only depends on the initial absolute velocity and tangential acceleration. It's true for all trajectories.

Vasily Mitch
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