How Long Does It Take a Train to Reach Twice Its Threshold Speed?

[bernvall]

Homework Statement

The resultant force acting on a train of mass m starting from rest on a level track is a constant P for speeds less than V . For speeds greater than V the power exerted by the resultant force has a constant value PV . Find the time taken to reach a speed 2V from rest, and the corresponding distance travelled.

Homework Equations

Force= power * velocity
Power= dw/dt

The Attempt at a Solution

for some reason, i don't know how to go about doing it.

 

[Andrew Mason]

Homework Statement

The resultant force acting on a train of mass m starting from rest on a level track is a constant P for speeds less than V . For speeds greater than V the power exerted by the resultant force has a constant value PV . Find the time taken to reach a speed 2V from rest, and the corresponding distance travelled.

Homework Equations

Force= power * velocity
Power= dw/dt

The Attempt at a Solution

for some reason, i don't know how to go about doing it.

Since W = Fs, Power = dW/dt = Force * ds/dt = Force * velocity

What does the resultant force do to the train? (hint: Newton's 2nd law). That should allow you to determine time and distance in reaching V in terms of P and m (mass of the train). Does anything change when it hits speed V?

AM

 

[bernvall]

Yes, i realized that i needed to use Newtons 2nd Law.

What i did was split it up in two, from 0 to V and then from V to 2V. the first part i managed to find the time and distance easily using equations of motion. However for the second part i didn't know what the resultant force was. It gives you the power at 2V NOT the resultant, so i got stuck again.

 

[Andrew Mason]

Yes, i realized that i needed to use Newtons 2nd Law.

What i did was split it up in two, from 0 to V and then from V to 2V. the first part i managed to find the time and distance easily using equations of motion. However for the second part i didn't know what the resultant force was. It gives you the power at 2V NOT the resultant, so i got stuck again.

Let speed = v. Since Power = PV = Fv for v>V, then what is the force F?

What is the kinetic energy at speed 2V? What is the relationship between change in kinetic energy, power and time where the power is constant? That should give you the time. And from that you should be able to work out the distance.

AM