# Some Problem Related to Position vs Time Graph

• shubham.bali7
In summary, the conversation discusses a player throwing a ball upwards with an initial speed of 29.4 m/s. The direction of acceleration during the upward motion is positive, and at the highest point of its motion, the velocity and acceleration of the ball are both positive. The conversation also mentions choosing a specific location and time for the ball at its highest point, and gives the signs of position, velocity, and acceleration during the upward and downward motion. Finally, the conversation mentions calculating the height the ball rises and the time it takes to return to the player's hands, assuming a downward acceleration of g = 9.8 m/s² and neglecting air resistance.
shubham.bali7
Hi

So Heres the Question:-
A player throws a ball upwards with an initial speed of 29.4 m s–1.
(a) What is the direction of acceleration during the upward motion of the ball ?
(b) What are the velocity and acceleration of the ball at the highest point of its
motion ?
(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its
highest point, vertically downward direction to be the positive direction of
x-axis, and give the signs of position, velocity and acceleration of the ball
during its upward, and downward motion.
(d) To what height does the ball rise and after how long does the ball return to the
player’s hands ? (Take g = 9.8 m s–2 and neglect air resistance).[/CENTER]

So my problem is in Part(c)
Answer Comes Out that in both cases(upward and downward) Acceleration is Positive..
but how? i mean shouldn't it be Negative in downward and Positive in upward motion

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They are positive provided downward direction is the positive axis. I just told acceleration is g downwards(or -g upwards)

In general, you can choose any direction you want to be positive. However, in part (c) they specifically say "Choose ... vertically downward direction to be the positive direction"

Last edited:
tnxxx... guyss... u helpd... :)

?

I understand your confusion regarding the direction of acceleration in this scenario. It is important to note that the direction of acceleration is determined by the direction of the net force acting on the object, not necessarily the direction of its motion. In this case, the net force acting on the ball is always directed towards the ground, regardless of whether it is moving upwards or downwards. This is due to the force of gravity, which is always pulling objects towards the center of the Earth.

Therefore, even though the ball is moving downwards, the acceleration is still directed towards the ground, making it positive. Similarly, when the ball is moving upwards, the acceleration is still directed towards the ground, making it positive as well.

In terms of position, velocity, and acceleration, it is important to define a reference point and direction. In this case, the reference point is the highest point of the ball's motion, and the positive direction is vertically downward. This means that the position, velocity, and acceleration of the ball will be negative during the upward motion and positive during the downward motion.

To calculate the height and time of the ball's motion, we can use the equations of motion, specifically the equation for displacement (s = ut + 1/2at^2) and the equation for time (t = (v-u)/a). Using the given values, we can determine that the ball reaches a maximum height of approximately 42.8 meters and returns to the player's hands after approximately 5.5 seconds.

I hope this explanation helps to clarify the direction of acceleration and the signs of position, velocity, and acceleration in this scenario. Remember, as scientists, it is important to carefully define our reference points and directions when analyzing motion.

## 1. What is a position vs time graph?

A position vs time graph is a visual representation of an object's position (y-axis) over time (x-axis). It shows how an object's position changes as time passes.

## 2. How do you interpret a position vs time graph?

To interpret a position vs time graph, you can look at the slope of the graph. A positive slope indicates that the object is moving in a positive direction, while a negative slope indicates movement in a negative direction. The steeper the slope, the faster the object is moving. Also, the y-intercept of the graph represents the initial position of the object.

## 3. What is the difference between a positive and negative slope on a position vs time graph?

A positive slope on a position vs time graph represents an object moving in a positive direction, while a negative slope represents movement in a negative direction. This means that the object is either moving away from the reference point (positive) or towards the reference point (negative).

## 4. How can you determine an object's velocity from a position vs time graph?

Velocity is defined as the rate of change of an object's position. On a position vs time graph, the velocity can be determined by calculating the slope at any given point. The slope represents the object's instantaneous velocity at that particular time.

## 5. Can a position vs time graph be used to determine an object's acceleration?

Yes, a position vs time graph can be used to determine an object's acceleration. The acceleration can be found by calculating the slope of the velocity vs time graph, which is the second derivative of the position vs time graph. The slope of the velocity vs time graph represents the object's instantaneous acceleration at that particular time.

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