Question

The equation r(t)= (2t)i + (2t-16t^2)j is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0.

Answer 1

Answer:

The answer is 135 degrees.

Step-by-step explanation:

As we are given the position. If we take the derivative, we get the velocity vector. If we take the derivative again, we find the acceleration vector of the particle.

$r(t)=(2t)i+(2t-16t^{2})j$

$V(t)=2i+(2-32t)j$

$a(t)=-32j$

At time t=0;

$v(t)=2i+2j$

$a(t)=-32j$

As i attach in the picture the angle between the velocity and acceleration vector is $(45+90)=135$ degrees