Your initial conditions for position are not your initial values for velocity.ana111790 said:position vector = [at - (bt^3)/3 + v_x(0)]i + [(ct^2)/2 + v_y(0)]j
position vector = [at - (bt^3)/3 + a]i + [(ct^2)/2]j
This however is the wrong answer and I don't know understand why?
out?
Integration is a mathematical process that helps in finding the original function from its derivative. In terms of finding position from velocity, integration helps by finding the displacement function from the velocity function.
Position is the location of an object in relation to a reference point, while velocity is the rate of change of an object's position over time. In other words, position tells us where an object is located, while velocity tells us how fast and in what direction it is moving.
No, position cannot be determined from velocity alone. Velocity only tells us about the rate of change of an object's position, but it does not give us the actual position. Integration of the velocity function is needed to find the position function.
Integration is used in many real-life scenarios, such as in physics, engineering, and economics, to calculate position from velocity. For example, it is used in calculating the position of a moving car, the displacement of an object under the influence of gravity, and the change in stock prices over time.
Yes, there are limitations to using integration to find position from velocity. One limitation is that the velocity function must be continuous and have a well-defined derivative. Additionally, integration can only give us an approximate position, as it is subject to errors in measurement and calculation.