Acceleration in respect to power, and a KE/momentum problem.

[blackwing1]

I was doing the IPhO F=ma test from 2008 and couldn't get these two questions.

Question 1

Homework Statement

A car has an engine which delivers a constant power. It accelerates from rest at time t = 0, and at t = t_0 its acceleration is a_0. What is its acceleration at t =2t_0? Ignore energy loss due to friction.

Homework Equations

Any non-calculus based equations.

The Attempt at a Solution

I reasoned that since the power was constant, then the work done on the wheels would also be constant as power = work/time. Then, since work = fd, the force would be constant and thus the acceleration would be constant. However, when I checked the answer, it said that the acceleration should actually be 1/(sqrt2)a_0 at that point. Is this due to rotation friction or something?

Question 2

Homework Statement

Consider a particle at rest which may decay into two daughter particles or into three daughter particles. Which of the following is true in the two body case but false in the three body case. (No external forces)

a. The velocity vectors of the daughter particles must lie in a single plane
b. Given the total kinetic energy of the system and the mass of each daughter particle, it is possible to determine the speed of each daughter particle.
c. Given the speeds of all but one daughter particle, it is possible to determine the speed of the remaining particle.
d. The total momentum of the daughter particles is zero.
e. None of the above.

Homework Equations

Any non-calculus based equations

The Attempt at a Solution

(The answer was b. I chose a.)
I first took out D because that would be true in both cases.
I then took out C because I think the mass is needed to solve that scenario, so it would work for neither case.
I initially took out B too, but in retrospect, I realized it works in the first case because you can solve it with conservation of momentum and conservation of KE (2 equations for 2 variables) but not the second case (2 equations for 3 variables.)
I am, however, still confused why a. doesn't work. When there's two rays originating from a single point, don't they have to be in a single plane?

Thanks for the help :D

 

[gneill]

I was doing the IPhO F=ma test from 2008 and couldn't get these two questions.

Question 1

Homework Statement

A car has an engine which delivers a constant power. It accelerates from rest at time t = 0, and at t = t_0 its acceleration is a_0. What is its acceleration at t =2t_0? Ignore energy loss due to friction.

Homework Equations

Any non-calculus based equations.

The Attempt at a Solution

I reasoned that since the power was constant, then the work done on the wheels would also be constant as power = work/time. Then, since work = fd, the force would be constant and thus the acceleration would be constant. However, when I checked the answer, it said that the acceleration should actually be 1/(sqrt2)a_0 at that point. Is this due to rotation friction or something?

Taking one question at a time...

What equations do you know concerning power and energy? How about power, force, and velocity? Kinetic energy and velocity? Acceleration and force? Listing the equations that you know may give you some ideas.

Assuming that NO energy is lost to any sort of friction, what's the expected kinetic energy of the car with respect to time? What can you then say about its velocity with respect to time?

 

[blackwing1]

Thanks for the help. I figured them out. Kind of surprised I hadn't seen the answers sooner. Pretty obvious in hindsight.