You have a remote-controlled car that has been programmed to have velocity v⃗ =(−3ti^+2t2j^)m/s, where t is in s. at t = 0 s, the car is at r⃗ 0=(3.0i^+2.0j^)mwhat is the x component of the car's position vector at 10 s? what is the y component of the car's position vector at 10 s? what is the x component of the car's acceleration vector at 10 s? what is the y component of the car's acceleration vector at 10 s?

The y-component of the car's position vector is 670m/s.

The x-component of the acceleration vector is -3, and the y-component is 40.

Explanation:

The displacement vector of the car with velocity

is the integral of the velocity.

Integrating we get the displacement vector :

Now if the initial position if the car is

then the displacement of the car at time is

Now at , we have

The y-component of the car's position vector is 670m/s.

The acceleration vector is the derivative of the velocity vector:

and at it is

The x-component of the acceleration vector is -3, and the y-component is 40.