Anet force of 50 n is applied to a 10 kg cart that is already moving at 3 m/s. the final velocity of the cart was 8 m/s. for how long was the force applied

1 second

Explanation:

Assuming that the force is in the same direction as speed we can do the graphic.

Draw the forces present on the problem (weight and the net force).Newton's second law. The summation of the forces is equal to the product between mass and aceleration.Plan the equation on x direction (because the mass is moving on that way). The result would be: From that equation we know that the aceleration is 5m/s2.Also, we know (because it is a uniform line movement) that the aceleration is related with the speed. Clearing the equation: And replacing: So, the force is applied for 1 second.