How to Solve a Spaceship Calculus Problem?

In summary, the conversation is about calculating the time it would take for a spaceship to reach the speed of light with a given acceleration rate. The speaker got an answer of 5 years, but is unsure if it is correct and is looking for a faster method to solve the problem. The other person suggests that it is a straightforward problem and can be solved by integrating acceleration and solving for time.
  • #1
JakePearson
52
0
if a spaceship accelerates, from rest at time t=0, at a rate of 2t / sqrt(1 + t2) ms-2 at time t, calculate in years to 1 significant figure how long it would take to reach the speed of light 3x108 ms-1?

i got an answer of 5 years, is this correct, but i have made a mess of my workings, what is the best way to answer this question in the shortest time period?

many thanks
 
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  • #2


How did you work it out? It's pretty straightforward, isn't it?
 
  • #3


This is a very straight forward problem.

All you need to know is that you get a velocity when you integrate acceleration respect to time.

After that, it's all algebra. plug-in, and solve for t.
 

FAQ: How to Solve a Spaceship Calculus Problem?

What is the "Spaceship calculus problem"?

The "Spaceship calculus problem" is a hypothetical scenario in which a spaceship is traveling at a constant velocity and encounters a sudden change in its acceleration. This problem is often used to illustrate the concepts of calculus, specifically the calculation of instantaneous velocity and acceleration.

Why is this problem important for scientists?

This problem is important for scientists because it demonstrates the real-world applications of calculus in understanding the motion of objects. It also helps scientists to develop mathematical models to predict and analyze the motion of objects in space.

How is calculus used to solve this problem?

Calculus is used to solve this problem by calculating the instantaneous velocity and acceleration at a specific moment in time. The derivative of the position function gives the instantaneous velocity, and the derivative of the velocity function gives the instantaneous acceleration.

What are some challenges in solving the "Spaceship calculus problem"?

One of the main challenges in solving this problem is accurately modeling the motion of the spaceship. In reality, there are many factors that can affect the motion of a spaceship, such as air resistance and gravitational pull from other planets. Additionally, the sudden change in acceleration can make the calculations more complex.

Are there any real-life examples of the "Spaceship calculus problem"?

Yes, there are many real-life examples of the "Spaceship calculus problem". For instance, when a rocket is launched into space, it experiences a sudden change in acceleration as it leaves the Earth's atmosphere. Another example is when a satellite orbits around a planet, it experiences a constant velocity but a changing acceleration due to the planet's gravitational pull.

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