Determine the velocity of the car after it has been floored for 8 seconds

[2Pac]

Hey if anyone could please tell me how to do this it would be a great help.

ok the question asks about an accelerating car. The mass of the car is 1200kg. When the engine is floored it creates a constant forward force of 9600N. The drag created by the car is equal to this equation: D=160v. Determine the velocity of the car after it has been floored for 8 seconds.

 

[Tide]

You just need to solve the equation of motion:

$$m\frac {dv}{dt} = 9600 - 160 v$$

Just remember to keep your units consistent!

 

[2Pac]

actually i am not familiar with that equation. and my calculus is poor. So if anyone could explain this further, thanks!

 

[HallsofIvy]

$$1200\frac {dv}{dt} = 9600 - 160 v= 160(60- v)$$
is the same as
$$\frac{dv}{60-v}= \frac{160}{1200}dt= \frac{1}{20}dt$$

To integrate the left side, let u= 60- v so that du= -dv and the equation becomes
$$-\frac{du}{u}= \frac{1}{20}dt$$

You ought to be able to integrate that.