Acceleration, magnitude, displacement.

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SUMMARY

The discussion focuses on calculating the acceleration and displacement of a spaceship accelerating in the positive x direction. The spaceship starts with an initial velocity of 150 m/s and reaches an instantaneous velocity of 1500 m/s after 25 seconds, at an angle of 55 degrees above the x-axis. The acceleration in the x direction (Ax) is calculated to be 54 m/s², while the magnitude of the displacement after 25 seconds is determined using the equation X = 1/2(Vo + V)t, yielding a displacement of 20625 m. The calculations reveal errors in the initial attempt, particularly in the use of trigonometric functions for velocity components.

PREREQUISITES
  • Understanding of kinematic equations for linear motion
  • Familiarity with vector decomposition and trigonometric functions
  • Knowledge of instantaneous velocity and acceleration concepts
  • Ability to apply the formula for displacement in uniformly accelerated motion
NEXT STEPS
  • Review kinematic equations, specifically the relationship between acceleration, velocity, and time
  • Study vector decomposition techniques to resolve velocities into components
  • Learn about the significance of angles in motion analysis, particularly in two-dimensional motion
  • Practice problems involving displacement calculations in accelerated motion
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Students studying physics, particularly those focusing on kinematics and motion analysis, as well as educators seeking to clarify concepts related to acceleration and displacement in two-dimensional motion.

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Homework Statement


a spaceship is observed traveling in the positive x direction with a speed of 150m/s when it begins accelerating at a constant rate. the spaceship is observed 25s later traveling with an instantaneous velocity 1500m/s at an angle of 55 degrees above the x+ axis. a.) calculate the acceleration of the spaceship in the x direction, Ax, and in the y direction, Ay, during 25 seconds. what was the magnitude of the spaceship's acceleration during the 25 seconds? b.) what was the magnitude of the displacement of the spaceship after 25 seconds?


Homework Equations


a= delta v/ delta t

X= 1/2(Vo+V)t


The Attempt at a Solution



for part a i attempted it but i didnt get anything right:

cos55((150m/s)/(150 m/s)) = .0574 in positive x direction.
sin55((150m/s)/(150 m/s)) = .0819 in positive y direction.

a= delta v/delta t
1500-150/25-0 = 1350/25 = 54 m/s^2

magnitude: 1500^2/150^2 =150^2/150^2 +b^2
= sq. root of 2250000-22500 = b
b= 1492 m/s

part b)
X= 1/2 (Vo+V)t
1/2(150+1500)25s
X= 20625 m/s^2 in positive x direction.
 
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please help me out with this. i want to know what i did wrong.
 
i was thinking for the acceleration part, maybe i am supposed to switch the values? so it would be 150-1500/0-25?
 

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