# Constant Power, Variable Acceleration

• cep
In summary, the conversation discusses a car's acceleration from rest on a straight track with constant engine power and negligible air resistance. The first question asks for the car's velocity as a function of time. The second question involves a second car starting from rest with constant acceleration and determining which car takes the initial lead and if the other car overtakes it. The third question involves a drag race with an opponent's car having a constant acceleration of 12.0 m/s2 and calculating the minimum engine power needed to win the race, assuming constant power output and a distance of 0.250 miles to the finish line. The equation used to solve these problems is P = dW/dt = F * delta-r = ma * delta-r =
cep

## Homework Statement

A car of mass m accelerates from rest along a level straight track, not at constant acceleration, but with constant engine power, P. Assume that air resistance is negligible.

a) Find the car's velocity as a function of time
b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens.
c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of 12.0 m/s2. Both cars have identical masses of 1000 kg. The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is 0.250 miles.

## Homework Equations

P=dW/dt; W=F [dot] delta-r; F=ma

## The Attempt at a Solution

I'm pretty stuck at this one. My first thought is dW/dt=F [dot] dr/dt = F [dot] v = Fvcos[F-v]=P, but since a (and therefore F) are variable, I'm not sure where to go from here. Once I get the answer to A, I think I can do B and C (though the acceleration isn't mentioned in B, which I find confusing). Any hints? Thanks :)

Constant power means that energy is being given to the car at a constant rate. Where is that energy going?

## What is constant power?

Constant power refers to a situation where the power output remains the same over time. This means that the amount of energy being transferred or converted per unit time remains constant.

## What is variable acceleration?

Variable acceleration refers to a situation where the rate of change of velocity (or acceleration) is not constant. This means that the velocity of an object is changing at a varying rate over time.

## How are constant power and variable acceleration related?

In order to maintain constant power, the force applied to an object must vary in proportion to its changing acceleration. This means that as the acceleration increases, the force must also increase to maintain a constant power output.

## What are some real-life examples of constant power, variable acceleration?

One example is a car traveling up a hill at a constant speed. As the car moves up the hill, the slope increases and the car's acceleration decreases. However, the engine must maintain a constant power output in order to keep the car moving at the same speed.

## How is constant power, variable acceleration used in scientific research?

This concept is commonly used in studying the motion of objects in different environments, such as air resistance or friction. By maintaining a constant power output, scientists can measure and analyze how an object's acceleration changes in different conditions.

Replies
3
Views
577
Replies
20
Views
1K
Replies
3
Views
764
Replies
5
Views
1K
Replies
5
Views
2K
Replies
9
Views
457
Replies
5
Views
2K
Replies
18
Views
3K
Replies
1
Views
3K
Replies
34
Views
4K