What Are the Calculations for Acceleration in These Linear Motion Problems?

In summary, linear motion is the movement of an object along a straight path where distance and displacement are the same. Examples include a car on a straight road, a rolling ball, and a person walking in a straight line. Linear motion differs from rotational motion in that it involves movement along a straight path and has a constant velocity. It is measured using units of distance and time, and its speed is typically measured in meters or feet per second. The laws of linear motion include Newton's first, second, and third laws.
  • #1
thermisius
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Homework Statement



2 linear motion problems

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hi i have 2 questions on linear motion that i could use some help on step by step.

1. Jules Verne in 1865 proposed sending men to the moon by firing a space capsule from a 220-m cannon with final velocity of 10.97 km/sec.. What would have been the unrealistically large acceleration experienced by the space travelers during launch? Compare your answer with the free-fall acceleration,9.8 m/sec.


2. A model rocket is launched straight upward with an initial speed of 50.0 m/sec.. It accelerates with a constant upward acceleration of 2.00m/sec2 until its engines stop at an altitude of 150 m. (a) what is the maximum height reached by the rocket? (b) how long after lift off does the rocket reach its maximum height? (c) How long is the rocket in the air?

Homework Equations



a= change in v/t d=averageV multiplied by time vf
d= 1/2a multiplied by t2 + vi multiplied by t + hi

The Attempt at a Solution


1. for number one i am stuck because all the question gives me is final velocity and i don't know how i can only use that to find the acceleration.

2. As for number two i plugged in the information in d= .5a multiplied by t + vi multiplied by t + hi

to get d= 1/2 (2m.) multiplied by sec2 + 50m/sec multiplied by sec. + 0
but I am confused on how to figure the answer because i get d=51m./sec2
 
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  • #2
oops put this under wrong category sry about that
 
  • #3
thermisius said:

Homework Statement



2 linear motion problems

--------------------------------------------------------------------------------

hi i have 2 questions on linear motion that i could use some help on step by step.

1. Jules Verne in 1865 proposed sending men to the moon by firing a space capsule from a 220-m cannon with final velocity of 10.97 km/sec.. What would have been the unrealistically large acceleration experienced by the space travelers during launch? Compare your answer with the free-fall acceleration,9.8 m/sec.


2. A model rocket is launched straight upward with an initial speed of 50.0 m/sec.. It accelerates with a constant upward acceleration of 2.00m/sec2 until its engines stop at an altitude of 150 m. (a) what is the maximum height reached by the rocket? (b) how long after lift off does the rocket reach its maximum height? (c) How long is the rocket in the air?

Homework Equations



a= change in v/t d=averageV multiplied by time vf
d= 1/2a multiplied by t2 + vi multiplied by t + hi

The Attempt at a Solution


1. for number one i am stuck because all the question gives me is final velocity and i don't know how i can only use that to find the acceleration.
You know the final velocity (vf= 10.97 km/sec), the initial velocity (vi= 0 km/sec), initial height (h= 0 km) and distance traveled (d= 220 m= .22 km). Use d= 1/2 a t2+ vit+ hi and vf= at. You have two equations for the two unknown values a and t.

[/quote]2. As for number two i plugged in the information in d= .5a multiplied by t + vi multiplied by t + hi

to get d= 1/2 (2m.) multiplied by sec2 + 50m/sec multiplied by sec. + 0
but I am confused on how to figure the answer because i get d=51m./sec2[/QUOTE]
The rocket accelerates at a= 2 m/s2 until it is 150 m high. That means
150= (1/2)(2)t2+ 50t Solve that for t to determine how long the rocket engine fires and then use vf= (2)t+ 50 to determine its speed at that time. After the rocket engine has stopped firing, its acceleration is that of gravity, -9.8 m/s2. Use d= (-9.8/2)t2+ vft+ 150 (vf is the speed after the rocket engine stopped firing that you just found) for its height after that. You can find its maximum value by completing the square.
 
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FAQ: What Are the Calculations for Acceleration in These Linear Motion Problems?

1. What is linear motion?

Linear motion is the movement of an object along a straight path, where the distance and displacement of the object are the same.

2. What are some examples of linear motion?

Some examples of linear motion include a car traveling down a straight road, a ball rolling across a flat surface, and a person walking in a straight line.

3. How is linear motion different from rotational motion?

Linear motion involves movement along a straight path, while rotational motion involves movement around an axis or point. Additionally, linear motion has a constant velocity, while rotational motion has a constant angular velocity.

4. How is linear motion measured?

Linear motion is measured using units of distance, such as meters or feet, and units of time, such as seconds or minutes. The speed of linear motion is typically measured in meters per second or feet per second.

5. What are the laws of linear motion?

The laws of linear motion include Newton's first law (an object at rest stays at rest and an object in motion stays in motion at a constant velocity unless acted upon by a net force), Newton's second law (force equals mass times acceleration), and Newton's third law (for every action, there is an equal and opposite reaction).

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