Position of a mouse is given x=10-2t+4t² and y=2+3t. What is the velocity and acceleration in unit vector notation? Here x and y

Question

Please help me to solve this math. I Know this app is for programming. Please help me with is problem

Answer 1

Though it's not really the place to talk about those problems, I'll still point you in the right direction.

As the velocity is a variation of position in relation to the time, we can obtain it by taking the first derivative of the position function by the time.
The same reasoning can be applied to the velocity to obtain the acceleration.

Then, as you're working in a 2d referential (x,y) it's up to you to see how you can transpose those results into a vector

Answer 2

Sorry , didn't get it.

Answer 3

You've got two functions describing the position of the mouse relatively to the time, on a 2d referential (so two independant axis/directions -> x and y)

Those are x(t) and y(t).

As the velocity represents a variation of a position during a certain amount of time, we can conceptually reduce that time to a value close to 0

That's the principle of derivation by the time (or at least part of it, but that doesn't matter here)

So the velocity on the axis x (respectively y) is dx/dt

You can apply the same reasoning to the acceleration as it represents a variation of velocity relative to time.

So the acceleration on the axis x (respectively y) is dv/dt, which is equal to d^2x/dt^2, which is the second derivative of the position relatively to the time.

Then, when you got those velocities and accelerations, don't forget that each of them belongs to a dimension (x or y), so you can group both accelerations and both velocities into two vectors.

Answer 4

If you're wondering how to do the maths, just look for the formulas of derivation of a polynomial function on Google

Answer 5

Thanks 😊... Much love ❤️

Answer 6

You're welcome !