Time, force, distance, acceleration

[furor celtica]

Homework Statement

A car of mass 1220 kg travels up a straight road which is inclined at an angle A to the horizontal, where sinA=0.05. The resistances to motion are modeled as a constant force of magnitude 1400 N. The car travels a distance of 25.8 metres whilst increasing its speed from 8ms^-1, at the point X, to 12 ms^-1 at the point Y. Calculate the work done by the car's engine in traveling from X to Y.
The car's engine works at a constant rate of 40 kW. Calculate the time taken to travel from X to Y.

Homework Equations

The Attempt at a Solution

For the first problem I got 100 658 watts, which is correct.
However I'm confused by the second.

Firstly I can use power= work/time to get time=100 658/40 000= 2.51645 seconds
But I can also use s=0.5(u+v)t to get time= (2x25.8)/(12+8)= 2.58 seconds
Where have I gone wrong?

 

[Delphi51]

Your calcs check out. It sure looked like an inconsistency in the given numbers but ...
Constant power implies that the car will not accelerate constantly because part of the power is proportional to velocity, P = F*v. The formula s=0.5(u+v)t only works for constant acceleration.

 

[vela]

Homework Statement

A car of mass 1220 kg travels up a straight road which is inclined at an angle A to the horizontal, where sinA=0.05. The resistances to motion are modeled as a constant force of magnitude 1400 N. The car travels a distance of 25.8 metres whilst increasing its speed from 8ms^-1, at the point X, to 12 ms^-1 at the point Y. Calculate the work done by the car's engine in traveling from X to Y.
The car's engine works at a constant rate of 40 kW. Calculate the time taken to travel from X to Y.

Homework Equations

The Attempt at a Solution

For the first problem I got 100 658 watts, which is correct.

The answer should be in joules, not watts.

However I'm confused by the second.

Firstly I can use power= work/time to get time=100 658/40 000= 2.51645 seconds
But I can also use s=0.5(u+v)t to get time= (2x25.8)/(12+8)= 2.58 seconds
Where have I gone wrong?

You're assuming the acceleration is constant, but it isn't. Remember that $P = \vec{F}\cdot\vec{v}$. If P is constant, as the car speeds up, F must decrease, so the car's acceleration is decreasing.

 

[furor celtica]

thanks for your time

 

[rwisz]

I would first commend the individual for successfully solving the first problem and obtaining the correct answer. I would then explain that for the second problem, there are two different methods being used to calculate the time taken to travel from X to Y. The first method, using power= work/time, is based on the power output of the car's engine. This method assumes that the engine is working at a constant rate throughout the journey. The second method, using s=0.5(u+v)t, is based on the distance traveled and the initial and final velocities of the car. This method assumes that the acceleration of the car is constant.

Both methods are valid and can be used to calculate the time taken. The slight difference in the calculated times may be due to the assumptions made in each method and the slight variations in the values used (e.g. rounding off). It is important to consider the assumptions and limitations of each method when solving a problem and to select the most appropriate method based on the given information. In this case, since the problem states that the car's engine works at a constant rate, using the first method may be more appropriate. However, if more information about the car's acceleration is given, the second method may be more accurate.