Final answer:
The acceleration and then using the mass of the cart, we can determine that a force of 12.9N is needed.
Step-by-step explanation:
To calculate the force needed to cause a cart to change its velocity, you can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the mass of the cart is 12kg and the change in velocity is from 3.5m/s to 7.8m/s, which is an increase of 4.3m/s. The time taken for this change is 4 seconds.
First, calculate the acceleration using the formula acceleration = change in velocity / time taken. In this case, the acceleration is 4.3m/s / 4s = 1.075m/s^2.
Now, use Newton's second law to find the force needed. Force = mass * acceleration.
Plugging in the values, we get Force = 12kg * 1.075m/s^2 = 12.9N.