When you receive your cart, we recommend starting out the first two weeks with short sessions of 15-20 minutes with rest periods in between. Even though your pet may not seem tired, he will be. This is a LOT of aerobic work.
It is especially important for older pets to start out this way. They need time to adjust and build up some endurance, both respiratory and cardiac. Their muscles need time to build also.
You can greatly speed up the adjustment time by sling walking your pet until your cart arrives. This will help them get the feel for the cart as well as building strength and endurance.
Once your pet is used to the added exercise, you may leave them in the cart for longer periods. If you see them attempting to lay down, that generally means it is time for a rest.
Pets who have been in carts for a long time can go for several hours. Our own dog, Mary our Schnauzer has now been in hers for over 7 years (2008) and she frequently spends half the day in her cart. No problem.

WE NEVER RECOMMEND LEAVING YOUR PET IN THE CART UNATTENDED. SUPERVISION IS NEEDED NO MATTER HOW LONG THEY HAVE BEEN USING A CART.