on a force-time graph:
rectangle is shaded in from 2 to 8 on the x axis. It is shaded from 0 to 8 on the y axis. (so the base is 2 to 8 and the height is 0 to 8)
The graph is for a force acting on a 12.0 kg cart initially at rest on a frictionless surface.
What is the final velocity of the cart?
Thank you for your help.
To determine the final velocity of the cart from the force-time graph, you would need to calculate the area of the shaded rectangle.
In this case, the base of the rectangle represents the time interval during which the force is acting on the cart, which is from 2 to 8 seconds.
The height of the rectangle represents the magnitude of the force, which is from 0 to 8 Newtons.
The area of the rectangle can be calculated by multiplying the base (in seconds) by the height (in Newtons):
Area = base × height
= (8 - 2) s × 8 N
= 6 s × 8 N
= 48 N·s
Now, to calculate the change in momentum of the cart, you can use Newton's second law of motion, which states:
Force = (change in momentum) / (change in time)
Since the force acting on the cart is constant in this case, you can rearrange the equation to solve for the change in momentum:
(change in momentum) = Force × (change in time)
Here, the force is the area of the rectangle, which is 48 N·s. The change in time is the time interval the force is acting on the cart, which is 8 - 2 = 6 seconds.
(change in momentum) = 48 N·s × 6 s
= 288 N·s
Now, using the equation for momentum:
Momentum = mass × velocity
We can rearrange the equation to solve for the final velocity of the cart:
velocity = (change in momentum) / mass
Here, the mass of the cart is given as 12.0 kg, and the change in momentum is 288 N·s.
velocity = 288 N·s / 12.0 kg
= 24 m/s
Therefore, the final velocity of the cart is 24 m/s.