Constant acceleration problem to find the speed of a rocket

In summary: Are you integrating over time, distance, or both? If you are integrating over time, then the limits would be the time at which the velocity equals zero. If you are integrating over distance, then the limits would be the distance at which the velocity equals zero.
  • #1
mahrap
37
0
A rocket starts from rest and moves upward from the surface of the earth. For the first 10 of its motion, the vertical acceleration of the rocket is given by 2.60t, where the -direction is upward.

What is the speed of the rocket when it is 240 above the surface of the earth?

v = v0 + at
change in x = (v + v0)t/2

I solved for t in the second equation by plugging in 240 for change in x, 0 for v0, and left v as v: meaning i solved for t in terms of v. Then i took this and plugged it in the t of the first equation with t=480/v, a=2.6(480/v) and v0=0. However i keep getting a wrong answer. What should i do?
 
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  • #2
mahrap said:
A rocket starts from rest and moves upward from the surface of the earth. For the first 10 of its motion, the vertical acceleration of the rocket is given by 2.60t, where the -direction is upward.

What is the speed of the rocket when it is 240 above the surface of the earth?

v = v0 + at
change in x = (v + v0)t/2

I solved for t in the second equation by plugging in 240 for change in x, 0 for v0, and left v as v: meaning i solved for t in terms of v. Then i took this and plugged it in the t of the first equation with t=480/v, a=2.6(480/v) and v0=0. However i keep getting a wrong answer. What should i do?

The acceleration is not constant, so the usual kinematic equations for constant acceleration will not apply. I see an integral or two in your future :smile:
 
  • #3
What would be the limits of my integration. How would I find the time where the rocket is at the given height to integrate the acceleration to get velocity?
 
  • #4
mahrap said:
What would be the limits of my integration. How would I find the time where the rocket is at the given height to integrate the acceleration to get velocity?

Integrate to find expressions for velocity as a function of time and distance as a function of time. Then use these expressions to solve the particular problem.

As for the limits, well what variable are you integrating over?
 
  • #5


I would suggest double-checking your calculations and making sure that all units are consistent. Additionally, it may be helpful to graph the velocity vs. time data and see if it follows a linear trend, which would indicate constant acceleration. If you are still having trouble, it may be helpful to seek assistance from a colleague or consult a physics textbook for guidance on solving constant acceleration problems.
 

FAQ: Constant acceleration problem to find the speed of a rocket

What is the constant acceleration problem for finding the speed of a rocket?

The constant acceleration problem for finding the speed of a rocket is a common physics problem that involves determining the speed of a rocket at a given time, given its initial speed and acceleration. It is often used to study the motion of objects in space.

How is acceleration defined in this problem?

In this problem, acceleration is defined as the rate of change of velocity over time. It is represented by the symbol "a" and is typically measured in meters per second squared (m/s^2).

What is the equation used to solve the constant acceleration problem?

The equation used to solve the constant acceleration problem is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time elapsed.

What is the difference between average acceleration and instantaneous acceleration?

Average acceleration is the total change in velocity divided by the total time elapsed, while instantaneous acceleration is the change in velocity at a specific moment in time. In the constant acceleration problem, we are typically dealing with average acceleration.

What are some common units used to express acceleration?

Some common units used to express acceleration include meters per second squared (m/s^2), kilometers per hour squared (km/h^2), and gravitational units (g). These units can be converted to each other using conversion factors.

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