An acceleration problem

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In summary, the conversation was about finding the instantaneous velocity at a given point on a velocity-time graph. The problem involved a model rocket accelerating vertically for 2.0 seconds, with known velocity data at specific time intervals. The speaker proposed representing the acceleration with a polynomial function and using the slope of the graph or the equation v = u + at to find the instantaneous velocity. The possibility of constant acceleration was discussed, and the conversation ended with a correction to a previous statement.
  • #1
This problem request the instanteous velocity at a given point which I have not yet discovered how to do, the problem is as follows...

The engine of a model rocket accelerates the rocket vertically upward for 2.0 s as follows: at t = 0, the rocket's speed is zero; at t = 1.0 s, its speed is 4.0 m/s; and at t = 2.0 s, its speed is 20 m/s. Plot a velocity vs. time graph for this motion.

I have found that the average acceleration during the 2.0 s interval is 10 m/s2

I am trying to find the instanteous velocity at 1.5. I know that i must find the slope of the line tangent to the point 1.5 on the graph but am having problms doing so. Any tips?
 
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  • #2
try representing the accln by a polynomial, in time.

Get this polynomial to fit the known data - i.e velocity at particular time invervals.
 
  • #3
Fermat said:
try representing the accln by a polynomial, in time.

Get this polynomial to fit the known data - i.e velocity at particular time invervals.

Since the velocity rate of change varies at the two intervals, and we are dealing with constant acceleration, then I assume you mean try to find two different lines for the two intervals and not one polynomial.

You need to find the slope of the velocity time surve between 0 and 1 second, the do the same for the interval of 1 to 2 seconds. Once you have this, read the graph and enjoy.


Regards,

Nenad
 
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  • #4
How do we know that the accln is constant ?
 
  • #5
Im assuming it is, but you might be right, since it is a rocket, acceleration might vary, but I doubt it since no mass is lost. Its not a momentum problem where they give you the mass flow rate out, I think its a simple kinematics problem, that's why I assumed constant acceleration.

Regards,

Nenad
 
  • #6
what about the instantaneous aceleration at 1.5?
 
  • #7
What about it, he needs to find instantaneous velocity at 1.5 seconds, not acceleration.

Regards,

Nenad
 
  • #8
If it's constant acceleration, there are a couple of ways.

You plotted the velocity-time graph - no ?
If so, then just read off the graph at t = 1.5s. You should get v = 12 m/s

Alternatively, you mentioned getting the slope of the graph between 1 and 2 secs.
let m be the slope. Then m = (v2 - v1)/(t2 - t1), where v1 is the velocity at t1 and v2 is the velocity at t2, and t1 = 1 sec and t2 = 2 sec.
This should give you m - the acceleration during the 2nd second of movement. Now simply use v = u + at over this movement.

If the accelerations aren't constant, and it is a rocket after all, then you can approximate its motion over the 2-second interval by a polynomial.

Let the velocity, v = at² + bt.
we have two data points, (1,4) and (2,20), where (x,y) == (time,velocity)
substituting for these data points in the eqn for velocity,

4 = a + b
20 = 4a + 2b

giving,

a = 6, b = -2

.: v = 6t² - 2t
v = 2t(3t - 1)
===========

at t = 1.5
v = 3(4.5 - 1)
v = 10.5 m/s
==========
 
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  • #9
Fermat said:
If it's constant velocity, there are a couple of ways.
Im assuming you meant to write "constant acceleration". The rest looks correct.

Regards,

Nenad
 
  • #10
Nenad said:
Im assuming you meant to write "constant acceleration". The rest looks correct.

Regards,

Nenad
Thanks for the note.

Edited my post
 

What is an acceleration problem?

An acceleration problem is a physics concept that describes the rate at which an object's velocity changes over time. It is often represented by the symbol "a" and is measured in units of meters per second squared (m/s²).

What causes an acceleration problem?

An acceleration problem can be caused by a number of factors, including forces acting on an object, changes in direction, or changes in speed. These factors can lead to an increase or decrease in an object's velocity and result in an acceleration problem.

How is an acceleration problem different from a velocity problem?

A velocity problem involves calculating the speed and direction of an object, while an acceleration problem involves calculating the rate of change of an object's velocity. In other words, velocity is a measure of how fast an object is moving, while acceleration is a measure of how quickly the object's velocity is changing.

What are some real-life examples of acceleration problems?

Some common examples of acceleration problems in everyday life include a car accelerating from a stop sign, a roller coaster speeding up as it goes down a hill, and a person jumping off a diving board into a pool. These situations all involve changes in velocity and therefore, acceleration.

How are acceleration problems solved?

To solve an acceleration problem, you will need to use the equation a = Δv/Δt, where "a" is acceleration, "Δv" is the change in velocity, and "Δt" is the change in time. You can also use other equations, such as Newton's second law, to solve for acceleration in specific scenarios.

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