Hi I have some graph problems I need help on.
Sketch a graph of velocity vs. time.
A cart is moving to the right on a horizontal surface while a constant net force of 3 newtons acts on it to the left. the force acting on the cart stops after a short period of time. At this time, the cart is still moving to the right.
A cart, starting at rest, is acted upon by a constant force of 3 newtons for 3 seconds at which point the force ceases.
Thank you
To sketch a graph of velocity vs. time, we need to understand the relationship between velocity and time for each scenario described.
In the first scenario, a cart is moving to the right initially while a constant net force of 3 newtons acts on it to the left. This force will cause the cart to decelerate until it comes to a stop. However, since the cart is still moving to the right at the time the force stops, it means that there is another force acting on it in the same direction, opposing the deceleration caused by the 3 newton force. As a result, the velocity of the cart remains constant even when the force stops.
To sketch the graph, we can assume that the velocity is in meters per second (m/s) and the time is in seconds (s). We can choose any scale and labeling for the axes as long as it is appropriate and understandable.
Start with the time axis (x-axis) and label it from 0 to a suitable value, such as 10 seconds. Then, label the velocity axis (y-axis) from a suitable negative value, such as -10 m/s, to a suitable positive value, such as +10 m/s.
At time t = 0, we know the cart is moving to the right, so its initial velocity can be positive, for example, 5 m/s. Plot a dot at (0, +5) on the graph.
From t = 0 onwards, the force of 3 newtons acts opposite to the motion of the cart, causing it to decelerate. The velocity will decrease linearly over time. You can plot additional dots at various points such as (1, +3), (2, +1), (3, 0), to represent the decreasing velocity until it reaches 0 m/s.
At the point when the force stops (let's assume it is at t = 3 seconds), the cart is still moving to the right. Therefore, after t = 3 seconds, the velocity should remain constant. You can continue the graph with a horizontal line at the value of velocity attained at t = 3 seconds. For example, if the velocity at t = 3 seconds is +1 m/s, you can draw a horizontal line at the y-value +1 from t = 3 seconds onwards.
In the second scenario, a cart starts at rest and is acted upon by a constant force of 3 newtons for 3 seconds, at which point the force ceases. Since the cart starts at rest, its initial velocity is 0 m/s.
Following the same steps as before, you can create the graph by plotting a dot at (0, 0) to represent the initial velocity.
During the period of 0 to 3 seconds, the cart is accelerating due to the force. The velocity will increase linearly over time. You can plot additional dots at various points such as (1, +1), (2, +2), (3, +3) to represent the increasing velocity until it reaches the final value.
At t = 3 seconds, the force ceases and the cart's velocity remains constant. You can continue the graph with a horizontal line at the final velocity value attained at t = 3 seconds.
Remember to label the axes and add a title to the graph to provide clarity.