Car Work, Acceleration and Power

In summary, a car with a mass of 1100 kg is accelerating from rest, with its acceleration increasing over time according to the expression: a = (1.160 m/s^3)t - (0.210 m/s^4)t^2 + (0.240 m/s^5)t^3. The work done on the car by the wheels during the interval from t = 0 to t = 3.00 s is ___________ J and the wheels' output power at t = 3.00 s is ___________ W. To determine the work, one can integrate the acceleration function to get the velocity function, then determine the kinetic energy at t = 3.
  • #1
yb1013
56
0

Homework Statement



As the driver steps on the gas pedal, a car of mass 1100 kg accelerates from rest. During the first few seconds of motion, the car's acceleration increases with time according to the expression below.

a = (1.160 m/s^3)t - (0.210 m/s^4)t^2 + (0.240 m/s^5)t^3

(a) What work is done on the car by the wheels during the interval from t = 0 to t = 3.00 s?

____________ J

(b) What is the wheels' output power at the instant t = 3.00 s?

___________ W


The Attempt at a Solution



Im really quite confused about this one... Although it seems like a problem where derivatives might be involved to simplify this a little more. Am I on the right track at all? Please Help??
 
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  • #2
How do you determine work? What is the formula?
 
  • #3
well W = P x t
 
  • #4
What about Force? Can't that give you the work?
 
  • #5
yea, W = F x d
 
  • #6
yb1013 said:
yea, W = F x d

There you go.

Now the car is accelerating isn't it? So it's applying a force to the car, the F = m*a kind of thing.

But it also does it over a distance covered in 3 sec.

So if there was only a way to figure the distance covered in 3 sec that might prove useful?
 
  • #7
i might be totally going the wrong route here but to get the distance part, can you just like take two anti-derivatives to bring it back to position which would give you distance??

also for the F=ma, how do you know what the acceleration is? can you just plug 0 and 3 into the equation and take the average of that?
 
  • #8
yb1013 said:
i might be totally going the wrong route here but to get the distance part, can you just like take two anti-derivatives to bring it back to position which would give you distance??

also for the F=ma, how do you know what the acceleration is? can you just plug 0 and 3 into the equation and take the average of that?

You're given the acceleration, so yes it looks like you can just integrate twice to determine x position distance at 3. You know initial condition is at rest.

Edit: Forgot you were trying to get to Work, so you can integrate once then for the Velocity function. Your work then should be equal to the kinetic energy at t=3 right?
 
  • #9
hmm, i did all that but it didnt come out right..
 
  • #10
Forgot you were trying to get to Work, so you can integrate once then for the Velocity function. Your work then should be equal to the kinetic energy at t=3 right?
 
  • #11
hmm maybe, alright well thanks for you help!
 

What is car work?

Car work refers to the amount of energy required to move a car from one point to another. It is typically measured in joules or foot-pounds.

What is acceleration?

Acceleration is the rate at which the velocity of a car changes over time. It is typically measured in meters per second squared (m/s²) or feet per second squared (ft/s²).

How is acceleration related to power?

Acceleration is directly related to power, as power is the rate at which work is done. The more power a car has, the faster it can accelerate.

What factors affect a car's acceleration?

Several factors can affect a car's acceleration, including its weight, engine power, and aerodynamics. The type and condition of the tires, as well as the road surface, can also impact acceleration.

What is the difference between horsepower and torque?

Horsepower and torque are two different measurements of power. Horsepower is a measure of the car's top speed, while torque is a measure of its ability to accelerate quickly. Horsepower is typically used to compare cars, while torque is more important for towing and hauling heavy loads.

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