I have a graph where the horizontal numbers are 0-9 which represents time (s) and the vertical numbers are 0 to -4, -2, 0, 2, 4, 6, 8 which represents position(m).
The question is: the position versus time for a certain object moving along the x-axis
The objects initial position is -2 m. Find the spontaneous velocity at 0.5 s. Answer in units m/s.
Find the instantaneous velocity at 2s. Answer in units of m/s.
Last problem for this homework assignment, need help!!!!
How come you have 10 x values and 8 y values?
That's the way the problem is given.
To find the spontaneous velocity at 0.5 s, we need to find the slope of the position-time graph at that specific time. The spontaneous velocity represents the rate at which the object is changing its position at that instant.
To find the instantaneous velocity at 2s, we need to find the slope of the position-time graph at that specific time. The instantaneous velocity represents the rate at which the object is changing its position at that precise moment.
Here's how we can find the answers:
1. Spontaneous Velocity at 0.5 s:
- Locate the point on the graph that corresponds to 0.5 s on the horizontal axis.
- Determine the position of the object at that time by finding the vertical value at that point on the graph.
- Take note of the position value.
- Find the position of the object at 0 s (the initial position) by using the given initial position (-2 m).
- Calculate the change in position by subtracting the initial position from the position at 0.5 s.
- Finally, divide the change in position by the time interval (0.5 s) to find the spontaneous velocity at 0.5 s. The resulting unit will be m/s.
2. Instantaneous Velocity at 2 s:
- Locate the point on the graph that corresponds to 2 s on the horizontal axis.
- Determine the position of the object at that time by finding the vertical value at that point on the graph.
- Take note of the position value.
- Find the position of the object at 0 s (the initial position) by using the given initial position (-2 m).
- Calculate the change in position by subtracting the initial position from the position at 2 s.
- Finally, divide the change in position by the time interval (2 s) to find the instantaneous velocity at 2 s. The resulting unit will be m/s.
It is important to note that to find the velocity at a specific time using a position-time graph, we calculate the average rate of change of position over a small time interval containing that specific time. This is why we need to use the change in position divided by the time interval between the two points.