An object has a position given by r = [2.0 m + (2.00 m/s)t] i + [3.0 m − (1.00 m/s^2)t^2] j, where quantities are in si units. what is the speed of the object at time t = 2.00 s?

1 m/s

Explanation:

We have an object whose position is given by a vector, where the components X and Y are identified by the unit vectors and (where each unit vector is defined to have a magnitude of exactly one):

On the other hand, velocity is defined as the variation of the position in time:

This means we have to derive :

This is the velocity vector

And when the velocity vector is:

This is the velocity vector at 2 seconds

However, the solution is not complete yet, we have to find the module of this velocity vector, which is the speed :

Finally:

This is the speed of the object at 2 seconds

c. magnitude and direction