# How to Calculate Car Acceleration from Power and Speed?

• g.uricchio
In summary, the car of mass 840.0 kg has a net power of 4300.0 W when it is accelerating at a speed of 10.4 m/s. To calculate the acceleration, we can use the equation P = Fv and solve for F. Then, we can use the formula F = ma to find the acceleration, which is equal to 5.1 m/s^2. The use of calculus and the chain rule can also help us find the acceleration by using the equation P = dE/dt = d/dt(.5mv^2) = .5m*2v*dv/dt = mva.
g.uricchio

## Homework Statement

A car of mass 840.0 kg accelerates away from an intersection on a horizontal road. When the car speed is 37.4 km/hr (10.4 m/s), the net power which the engine supplies is 4300.0 W (in addition to the extra power required to make up for air resistance and friction). Calculate the acceleration of the car at that time.

## Homework Equations

Work=Force*Distance

Power=Work/Time

Force=Mass*Acceleration

## The Attempt at a Solution

I have tried numerous ways of solving this problem and remain unsuccessful. My closest attempt was using the equation Power=Kinetic Energy/Time, I used the velocity as Kinetic Energy to find the time and plugged that into the Kinematic equation Vf=Vi+a*d but that did not work either. Please help me!

Do you know some calculus?
It looks like a calculus problem to me.
You can't use Power = KE/time: consider the situation where the car is moving at zero acceleration and a large speed. The power required ("extra" not counted as stated in problem) is zero but the KE is large.

Instead, you should use Power = dE/dt, the derivative of kinetic energy with respect to time. The differentiation is not difficult, but does involve the chain rule.

yes I do know calculus, I am in Calc 2 but I still don't follow.

M= 840.0 kg
P= 4300.0 W
v= 10.4 m/s

s = v*dt [you are working with power (which is watt per second). what should dt be?]

gives s

p = w/dt

gives w

w = f*s

gives f

f = m*a

how am I supposed to find dt when I am not given a time

As I recall power is equal to force times velocity.

Units of Watts = N-m/s

P = F*V

So the instantaneous power is given as 4300 w and the velocity is 10.4 m/s.

That makes F = 4300/10.4 doesn't it?

And you have the mass, so ...

i thought that power was equal to F*V but if you do the math it delivers units of Kg*m/s and not Kg*m/s2. maybe I am using the wrong velocity?

Watt = J/s = kgm2/s3 = Nm/s

So it works out just fine. :)

Oh, clever to remember P = Fv !

Just for interest, I was thinking of P = dE/dt = d/dt(.5mv^2) = .5m*2v*dv/dt = mva
which is the same as P = Fv.

## 1. How do you calculate the power of a car?

The power of a car can be calculated by multiplying the force applied to the car by its velocity. This can be represented by the equation P = F x v, where P is power in watts, F is force in Newtons, and v is velocity in meters per second.

## 2. What is the difference between horsepower and torque in car work and power calculations?

Horsepower is a measure of the rate at which work is done, while torque is a measure of the twisting force that causes rotation. In car work and power calculations, horsepower is used to determine the overall power of the car, while torque is used to measure the car's ability to accelerate and tow heavy loads.

## 3. How does engine size affect a car's work and power?

Generally, the larger the engine size, the more power a car will have. This is because a larger engine is able to produce more force and therefore, more power. However, other factors such as engine design and technology can also affect a car's work and power.

## 4. Can you calculate a car's work and power without knowing its engine size?

While engine size is an important factor in calculating a car's work and power, it is not the only factor. Other variables such as weight, aerodynamics, and gear ratios also play a role. Therefore, it is possible to estimate a car's work and power without knowing its engine size, but it may not be as accurate.

## 5. What is the significance of work and power in car performance?

Work and power are important factors in determining a car's performance. A car with high power and torque can accelerate quickly and tow heavy loads, while a car with low power may struggle. Work is also important in measuring a car's efficiency and fuel consumption. Generally, a car with higher power and lower weight will have better performance.

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