Trying to find the velocity of the center of mass. In the first half of the problem, I determined that a truck (m=2000kg, v=8.0m/s) and a car (m=1000kg, v=0, a=4.0m/s^2) have a center of mass at x=22 meters at t=3.0s.

I tried to get the answer by summing the forces on the vehicles on the left, and setting them equal to the total mass times the acceleration of the center of mass. So:

4.0m/s^2(1000kg)=3,000kg*a

From that, I have the acceleration of the cm as 1.3m/s^2. Then, plugging it in to v_f^2=v_i^2+2as, I get the velocity of the cm as 6.8 m/s. Unfortunately, the book says 9.3m/s.

Question

Trying to find the velocity of the center of mass. In the first half of the problem, I determined that a truck (m=2000kg, v=8.0m/s) and a car (m=1000kg, v=0, a=4.0m/s^2) have a center of mass at x=22 meters at t=3.0s. 

I tried to get the answer by summing the forces on the vehicles on the left, and setting them equal to the total mass times the acceleration of the center of mass. So:

4.0m/s^2(1000kg)=3,000kg*a

From that, I have the acceleration of the cm as 1.3m/s^2. Then, plugging it in to v_f^2=v_i^2+2as, I get the velocity of the cm as 6.8 m/s. Unfortunately, the book says 9.3m/s.

anonymous · Answer

Sorry, the way I wrote it was probably too abbreviated. I'm doing this from memory, so here goes. A truck and car, of masses 2000kg and 1000kg, respectively, depart from a stoplight at the same time. The truck has an initial v of 8m/s. The car's initial v is 0. The car accelerates at a rate of 4.0m/s^2. Find the center of mass and the velocity of the center of mass at t=3.0s.

anonymous · Answer

Beautiful, thank you. I'll need to take a closer look when I get home.