If the kinetic energy of an object has increased by 16 times, by how many times has its speed increased?

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.