A frictionless roller coaster ride is given a certain velocity at the start of the ride. At which point in the diagram is the velocity of the cart the greatest? Assume a frictionless surface. 
[asy]pair A = (1.7,3.9);
pair B = (3.2,2.7);
pair C = (5,1.2);
pair D = (8,2.7);

size(8cm);
path boundary = (0,0.5)--(8,0.5)--(8,5)--(0,5)--cycle;
path track = (0,3.2)..A..(3,3)..B..(4,1.8)..C..(6,1.5)..(7,2.3)..D;
path sky = (0,5)--track--(8,5)--cycle;

for (int a=0; a<=8; ++a) { draw((a,0)--(a,5), black+1); }
for (int a=0; a<=5; ++a) { draw((0,a)--(8,a), black+1); }
for (int a=-100; a<=100; ++a) { draw((0,a)--(8,a+8)); }
for (int a=-100; a<=100; ++a) { draw((8,a)--(0,a+8)); }

fill(sky,white);
draw(track, black+3);
clip(boundary);

label("$A$", A, dir(120));
label("$B$", B, dir(60));
label("$C$", C, dir(90));
label("$D$", D, dir(135));[/asy]
$ \textbf {(A) } \text {A} \qquad \textbf {(B) } \text {B} \qquad \textbf {(C) } \text {C} \qquad \textbf {(D) } \text {D} \\ \textbf {(E) } \text {There is insufficient information to decide} $ 

[i]Problem proposed by Kimberly Geddes[/i]
1. **Identify the principle of conservation of energy**: In a frictionless system, the total mechanical energy (sum of kinetic and potential energy) remains constant. This principle can be expressed as:
   \[
   E_{\text{total}} = KE + PE = \text{constant}
   \]
   where \( KE \) is the kinetic energy and \( PE \) is the potential energy.

2. **Express kinetic and potential energy**:
   - Kinetic energy (\( KE \)) is given by:
     \[
     KE = \frac{1}{2}mv^2
     \]
     where \( m \) is the mass of the cart and \( v \) is its velocity.
   - Potential energy (\( PE \)) is given by:
     \[
     PE = mgh
     \]
     where \( m \) is the mass of the cart, \( g \) is the acceleration due to gravity, and \( h \) is the height above a reference point.

3. **Analyze the relationship between kinetic and potential energy**: Since the total energy is conserved, an increase in kinetic energy must correspond to a decrease in potential energy, and vice versa. Therefore, the velocity of the cart is maximized when its kinetic energy is maximized, which occurs when its potential energy is minimized.

4. **Determine the point of minimum potential energy**: The potential energy is minimized when the height \( h \) is minimized. By examining the diagram, point \( C \) is the lowest point on the track.

5. **Conclusion**: Since the potential energy is minimized at point \( C \), the kinetic energy is maximized at this point. Therefore, the velocity of the cart is greatest at point \( C \).

\[
\boxed{\text{C}}
\]