Final answer:
The speed of the cart when it has been pushed 8.0 m is 0.5 m/s.
Step-by-step explanation:
To find the speed of the cart when it has been pushed 8.0 m, we can use the equation: Speed = Distance / Time. Since a constant horizontal force of 10 N is applied to the cart and friction is negligible, there is no change in kinetic energy and no work is done on the cart. Therefore, the speed of the cart will simply be the distance pushed divided by the time taken.
Assuming the force is applied continuously, we can calculate the time using the equation: Force = Mass × Acceleration. Rearranging for acceleration and substituting the known values, we find that the acceleration is 0.5 m/s2. We can use this acceleration to calculate the time taken using the equation: Time = Distance / Speed.
Substituting the known values, we find that the time taken is 16 seconds. Finally, we can substitute the known values for distance and time into the equation: Speed = Distance / Time. Substituting values, we find that the speed of the cart when it has been pushed 8.0 m is 0.5 m/s.