position versus time and velocity graph for collision of carts.?

Question

Consider a head-on collision between two dynamics carts. One is initially at rest and the other is moving (towards the cart at rest) at a constant velocity. Sketch a position vs. time plot for each cart before and after the collision (one plot for each ball that includes time before and after the collision).

Also can you describe the velocity vs time graph as well?

Obviously you can't draw it, so maybe describe what it would be like? thanks

Answer 1

The shape of the plots depends on whether it's elastic or not and the ratio of the masses. For the simplest case, two equal masses in a perfectly elastic collision, it's like the "Newton's balls" toy: all of ball 1's velocity V is transferred to ball 2. So the two plots of position vs. time superimposed ("co-plotted") would look like a horizontal (0 velocity) line crossed by a line or "ramp" with slope = V. The ramp and horizontl intersect at the time of collision. The plot for ball 1 is the ramp until the collision, then horizontal. The plot for ball 2 is horizontal until the collision, then the ramp
If we now specify that the collision is inelastic, the balls stick together and continue at V/2. Thus the coplot changes so that after the collision, both the horizontal portion and the ramp with slope V are replaced by a ramp with slope V/2, shared by both plots.
Next we restore elasticity but make the masses unequal, After the collision, the balls continue with unequal velocities. So the post-collison coplot looks like two ramps of different slope. If mass1 < mass2, ball 1 bounces backward, so ball 1's ramp will have the opposite slope of ball 2.

Answer 2

Acceleration speed = speed and direction of circulate, so which you additionally can say replace of place. Which leaves only acceleration. nicely, thats approach of removing, yet nevertheless the terrific answer, yet not for the terrific motives.