Interpreting Velocity graphs

In summary, the problem provides a velocity graph for a car starting at a position of 10m at time 0s. The graph shows the car decelerating with a constant slope. The question asks for the car's position at t = 2s, 3s, and 4s, and also if the car ever changes direction and at what time. To solve for the position, one can use the equation v=d/t or v=change in distance/change in time. By plugging in the given values, the car's position at t=2s is found to be 8m. However, this does not align with the fact that the car starts at 10m and adds distance as it moves.
  • #1
kraaaaamos
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Homework Statement



5. A car starts from xi = 10m at ti = 0s and moves with the velocity graph shown in figure on the right.
a. What is the object’s position at t = 2s, 3s, and 4s?
b. Does this car ever change direction? If so, at what time?

Homework Equations



V = d/t

The Attempt at a Solution



for t at 2 secs...
according to graph v= 4m/s

so position (d) = (t)(v)
= (2)(4)
= 8m?

am i doing it right?


OR

v = change d/change t
4m/s = (x-10)/(2-0)
4m/s = (x-10)/(2)
8m/s = x-10
x = 18m

is that correct?
 

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  • #2
for t at 2 secs...
according to graph v= 4m/s

so position (d) = (t)(v)
= (2)(4)
= 8m?

am i doing it right?
Well this can't be right if the car starts at 10 m and adds distance. The slope of the plot of velocity vs time is negative, which indicates the car is decelerating, and the since the slope is constant, the deceleration is constant.

Certainly when the car has a negative velocity, it is reversing.

Is one familiar with integration?

if v(t) = d x(t)/dt, then

x(t) = [tex]\int_0^t\,v(t) dt\,+\,x(0)[/tex]

This might be useful:

http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html
 
  • #3


I would first clarify the units for the velocity graph shown in the figure. Is it in meters per second (m/s) or kilometers per hour (km/h)? This information is important for accurately interpreting the graph.

Assuming the units are in m/s, here is my response:

a. According to the graph, at t = 2s, the car's position is at x = 18m. At t = 3s, the car's position is at x = 22m. At t = 4s, the car's position is at x = 26m.

b. Yes, the car does change direction. This can be seen on the graph where the velocity changes from positive to negative. This change in direction occurs at t = 3s.
 

1. What is a velocity graph?

A velocity graph is a visual representation of an object's velocity over a period of time. It shows how the object's velocity changes, either increasing or decreasing, over the given time frame.

2. How is velocity measured on a velocity graph?

Velocity is measured on the y-axis of a velocity graph, usually in meters per second (m/s). The x-axis represents time, with each interval on the axis corresponding to a specific time increment.

3. What is the difference between a positive and negative slope on a velocity graph?

A positive slope on a velocity graph indicates that the object is moving in the positive direction (such as to the right or upwards) and its velocity is increasing. A negative slope indicates that the object is moving in the negative direction (such as to the left or downwards) and its velocity is decreasing.

4. How can I determine an object's acceleration from a velocity graph?

Acceleration can be determined by calculating the slope of the velocity graph. The steeper the slope, the greater the acceleration. A horizontal line on the velocity graph indicates constant velocity and therefore zero acceleration.

5. Can a velocity graph show changes in direction?

No, a velocity graph only shows changes in an object's velocity over time. Changes in direction are represented on a separate graph, such as a position vs. time graph.

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