The graph shows the speed of the cart with three different fan speeds. which line represents the cart with the greatest acceleration? what is the fan speed for this cart? which line represents the cart with the least acceleration? what is the fan speed for this cart?

1) Which line represents the cart with the greatest acceleration?
The line that represents the cart with the greatest acceleration is the line corresponding to cart C (green line).
In fact, the acceleration is defined as the variation of speed per unit time:

and this corresponds to the slope of the line: the higher the slope, the larger the acceleration.

2) What is the fan speed for this cart?
It depends on the time at which we calculate it. For instance, if we take the point at t=5 s, we see that the fan speed is (green light) 160 cm/s.

3) Which line represents the cart with the least acceleration?
The line that represents the cart with the least acceleration is the blue line (cart A): as we said at point 1), the higher the slope, the larger the acceleration, so the cart with the least acceleration is the one with the smallest slope, which is the blue line.

4) What is the fan speed for this cart?
Again, it depends on which time we calculate the speed at. For instance, if we take again the point at t=5 s, we see that the speed of the fan is (blue line) 90 cm/s.