Question

Your 1500kg car is stuck behind a truck traveling 27 m/s. To pass it, you speed up to 34 m/s in

6.0 s. What power is required to do this?

Answer 1

P = 53375[W]

Step-by-step explanation:

First, we must use the following equation of kinematics, which allows us to calculate the acceleration value.

`v_(f)=v_(o)+a*t`

where:

Vf = final velocity = 34 [m/s]

Vo = initial velocity = 27 [m/s]

a = acceleration [m/s²]

t = time = 6 [s]

Now replacing:

`34=27+a*6\\a=1.167[m/s^(2) ]`

Now we must use Newton's second law, which tells us that the sum of forces is equal to the product of mass by acceleration. In this way, we have the following equation.

ΣF =m*a

where:

F = force [N]

m = mass = 1500 [kg]

a = acceleration = 1.167 [m/s²]

`F=1500*1.167\\F=1750[N]`

Power is defined as the product of force by speed. But we have two speeds, the initial and the final. We must use the average speed to be able to estimate the power needed.

`V_(average)=(34+27)/(2) =30.5[m/s]`

And the power:

`P=F*V_(average)\\P=1750*30.5\\P=53375[W]`