An insect flying away from a flower is in the position . Find the velocity vector, the speed, the acceleration vector and the size of the acceleration, all when .
You can find the velocity vector by differentiating the position vector . That gives you
Next, you can insert into to find the velocity vector at .
From here it’s easy to find the speed as well, as it’s just the length of the velocity vector . That means you have
Moving on, the acceleration is the derivative of the velocity vector
. You will see that there are no variables left after you perform this differentiation, which means that the acceleration is constant. This is the result:
The length of that vector is
giving you an acceleration of .