Drag Racing - Involving Work and Velocity

[marcus1255]

Homework Statement

The problem reads:

"You are stopped at a red light, an identical car to yours pull up alongside. When the light turns green, you and the other car accelerate at a constant rate, but the other car's acceleration is greater. You see another stop light ahead and know you will have to stop at the light, so you accelerate from 0 to 20 mph for half the distance and then brake slowly so you decelerate for the last half, you observe this takes you a total of 30 seconds. The other car accelerates from 0 to 40 mph for the first half of the distance and brakes for the last half. Both cars traveled the same distance, starting from rest and ending at rest. You want to know how much work your car engine did compared to the other car and how much work your brakes did compared to the other car"

Homework Equations

Acceleration = change in velocity / change in time
Work = Force x Distance

The Attempt at a Solution

I am not really sure where to start..

 

[Delphi51]

Convert to metric units. Do the motions one at a time, beginning with the acceleration from 0 to 20. There evidently is no friction loss, so you can just use energy formulas like KE = ½mv².

 

[kerimek]

I can provide a response to the problem by using the equations and principles of physics. First, let's define some variables:

a1 = acceleration of your car
a2 = acceleration of the other car
v1 = final velocity of your car
v2 = final velocity of the other car
d = distance traveled by both cars
t = time taken for both cars to travel the distance

Using the equation for acceleration, we can say that:

a1 = (v1 - 0) / (t/2) = 2v1/t
a2 = (v2 - 0) / t = v2/t

Now, we know that both cars traveled the same distance, so we can equate their velocities:

v1 = v2

Substituting this into the equations for acceleration, we get:

a1 = 2v1/t
a2 = v1/t

Now, let's look at the work done by the engine and brakes for each car. Work is equal to force multiplied by distance. In this case, the force is the same for both cars, as they are accelerating at a constant rate. So we can say that:

Work done by engine = Force x Distance = ma x d

For your car, the distance traveled is d/2 (since you accelerate for half the distance and then decelerate for the other half). So the work done by your engine can be calculated as:

Work done by your engine = ma1 x d/2 = m(2v1/t) x d/2 = mv1d/t

Similarly, for the other car, the work done by the engine can be calculated as:

Work done by other car's engine = ma2 x d = mv1d/t

We can see that the work done by the engine for both cars is the same, as they have the same mass, acceleration, and distance traveled.

Now, let's look at the work done by the brakes. The work done by the brakes is equal to the force applied by the brakes multiplied by the distance over which the brakes are applied. In this case, the force applied by the brakes is equal to the mass of the car multiplied by its deceleration. So we can say that:

Work done by brakes = Force x Distance = ma x d/2

For your car, the work done by the brakes can be calculated as:

Work done by