17. A 5.6 kg toy race car moves along an x axis. The diagram below shows the force acting on the car. (The vertical axis is marked in increments of 2 N.)
a) What is the momentum of the car at t = 9.0 s
b) What is the car's velocity at t = 9.0 s?
The graph has the following coordinates:
time force
sec newtons
1 2
2 4
3 4
4 4
5 2
6 0
7 -2
8 -2
9 0
To find the momentum of the car at t = 9.0 s, we first need to find the net force acting on the car at that time. We can do this by looking at the graph.
From the graph, we can see that the net force acting on the car is 0 N at t = 9.0 s. This is because the force is equal to 0 N at that time.
The momentum of an object is defined as the product of its mass and velocity. Since the net force is 0 N, the velocity of the car remains constant at t = 9.0 s.
Thus, to find the momentum of the car at t = 9.0 s, we can use the formula:
Momentum = Mass × Velocity
We are given the mass of the car as 5.6 kg. To find the velocity, we need to look at the graph again.
At t = 9.0 s, the force acting on the car is 0 N. We can see from the graph that the car's force was decreasing from 2 N to -2 N in the previous time intervals. Since the force is decreasing, the car's velocity is also decreasing.
To determine the velocity at t = 9.0 s, we can look at the trend in force values before and after that time. From the graph, the force was decreasing from 2 N to -2 N between t = 1.0 s and t = 8.0 s. Therefore, we can conclude that the velocity of the car is decreasing from t = 1.0 s to t = 8.0 s.
Since the velocity remains constant at t = 9.0 s, we can conclude that the car's velocity at that time is the same as its velocity at t = 8.0 s, which is -2 m/s. Thus, the car's velocity at t = 9.0 s is -2 m/s.
Now, we can plug the values into the momentum formula:
Momentum = Mass × Velocity
Momentum = 5.6 kg × (-2 m/s)
Momentum = -11.2 kg·m/s
Therefore, the momentum of the car at t = 9.0 s is -11.2 kg·m/s.
To summarize:
a) The momentum of the car at t = 9.0 s is -11.2 kg·m/s.
b) The car's velocity at t = 9.0 s is -2 m/s.