I built a railway where a chest cart stops on a non-powered powered rail under a hopper, and when the hopper is empty a redstone current is applied to the powered rail to make the cart move forward.
It stops under the hopper but when the redstone signal is applied it doesn't move.
I have tried this without the hopper and applying the redstone with a lever, but it still won't make the cart start moving again.
From the Minecraft Wiki:
"A rail in the "on" state will accelerate a minecart if any of the following is true:
1. The minecart is already moving, in which case the cart is accelerated in the direction of motion
2. The minecart is stationary, but one end of the powered rail is up against a solid block. In this case, the cart is accelerated in the direction that is not blocked.
3. The minecart is stationary, but the powered rail is on a slope. The instant the powered rail is activated, the brake is released and the cart will start moving down due to gravity. As the cart is now moving, rule (1) applies and the cart is accelerated in that direction."