# Calculating the speed using Potential graph

• Physicslearner500039
In summary, the conversation discusses the motion of a positron through a field with varying potential. The questions ask about the positron's speed and if it emerges from the field at a specific point. The conclusion is that the positron will continue with the same speed and may not immediately emerge from the field.
Physicslearner500039
Homework Statement
A positron (charge +e, mass equal to the electron mass) is moving at 1.0 X 107 m/s in the positive direction of an x axis when, at x = 0, it encounters an electric field directed along the x axis. The
electric potential V associated with the field is given in Fig. 24-52. The scale of the vertical axis is set by Vs = 500.0 V. (a) Does the positron emerge from the field at x = 0 (which means its motion is reversed) or at x = 0.50 m (which means its motion is not reversed)? (b) What is its speed when it emerges?
Relevant Equations
NA

My attempt, pictorially it looks like

I am confused with the questions (a). Does the positron emerge from the field at x =0? There is no potential at x=0, so the positron will continue with the same speed hence its motion is not reversed.
For the (b). The maximum volt is 200V, if i apply the Ui+Ki = Uf+Kf;

0.5*mp*v_ini^2 = 500*e + 0.5*mp*v_fin^2; mp -> mass of proton, v_init = 1*10^7m/s

0.5*1.67*10^-27 * 10^14 = (500*1.69*10^-19) + (0.5*1.67*10^-27*V_fin^2)

Solving for V_fin = 9.9*10^33 m/s; The positron continues with this speed. Even the constant potential of 500V is applied continuously from 0.2m to 0.5m why the speed is not decreasing? Please advise.

Physicslearner500039 said:
Does the positron emerge from the field at x =0? There is no potential at x=0, so the positron will continue with the same speed
It does not mean immediately. It is asking whether the positron makes it through or gets reflected somewhere along the field.

## 1. How do you calculate the speed using a potential graph?

To calculate the speed using a potential graph, you need to find the slope of the graph at a given point. The slope represents the rate of change of potential energy with respect to displacement, which is equal to the kinetic energy of the object. Therefore, the slope can be used to calculate the speed of the object at that point.

## 2. What is the relationship between potential energy and speed on a graph?

The potential energy and speed on a graph have an inverse relationship. As the potential energy increases, the speed decreases, and vice versa. This is because as the object moves towards a region of higher potential energy, it loses kinetic energy and its speed decreases.

## 3. Can a potential graph be used to calculate the speed at any point along a trajectory?

Yes, a potential graph can be used to calculate the speed at any point along a trajectory. This is because the slope of the graph at any point represents the speed of the object at that point. However, the accuracy of the calculation may vary depending on the complexity of the trajectory and the precision of the graph.

## 4. How can the potential graph be used to determine the maximum speed of an object?

The maximum speed of an object can be determined by finding the steepest slope on the potential graph. This represents the point where the object has the highest kinetic energy and therefore, the maximum speed. However, it is important to note that this only applies to conservative systems where energy is conserved.

## 5. What are the limitations of using a potential graph to calculate speed?

One limitation of using a potential graph to calculate speed is that it only applies to conservative systems where energy is conserved. In non-conservative systems, such as those with friction or air resistance, the potential graph may not accurately represent the speed of the object. Additionally, the accuracy of the calculation may be affected by the precision of the graph and the complexity of the trajectory.

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