# Can I get help with a car speed question? (to fight a traffic ticket)

1. May 17, 2015

### LaureeF

Can any one tell me how much the speed of a car going 60 mph would slow down going up a 30 degrees incline?

2. May 17, 2015

### smileandbehappy

It depends on how much force was driving the car doesn't it... :)

Do you mean how much the car could decelerate? If you take gravity and use some right angled triangles you can work that out simply enough. If you mean other things then you don't have enough information. How much a car would slow down to me could be deceleration or final velocity after some distance.

3. May 17, 2015

### billy_joule

Having driven up the worlds steepest street myself (19 degrees)
http://en.wikipedia.org/wiki/Baldwin_Street

I can safely say that transitioning to a 30 deg slope at 60 mph would be quite violent and likely result in damage to both yourself and your car, you may want to borrow a friends car and hire a stunt man, good luck

4. May 17, 2015

### davenn

yup it's a steep one
That's my ol' home town

and to the OP ... yes, agreed, way too little information so far from you

5. May 17, 2015

### LaureeF

Thank you for responding. The truth is I need the information to fight a traffic ticket. The car was completely stopped. Then with normal acceleration it traveled 200 yards up a 30 degree incline. At the 200 yard mark a policeman said I was doing 67 mph. Aside from absolutely knowing that the top speed I reached was 53 mph, I am trying to prove that my car could not have reached 67 mph starting from zero in 200 yards going uphill at a 30 degree angle. It's not like it is a sports car. It's a Toyota Matrix - not exactly a speedy car. And I'm 68 years old. I'm almost never in a hurry anymore. Lauree

6. May 17, 2015

Staff Emeritus
I think you need to remeasure some things - in particular the 30 degree angle. 200 yards at 30 degrees means you would be thirty stories up at the end.

7. May 18, 2015

### OCR

8. May 18, 2015

### LaureeF

You're right!! It's only 3 degress, not 30 degrees. Little mistake (lol). Thanks.

9. May 18, 2015

Staff Emeritus
I still think you need to remeasure things. 0-53 in 200 feet implies a 0-60 time of 5.8 seconds. While there are vehicles that can do that, the Toyota Matrix is not one of them.

10. May 18, 2015

### cjl

To be fair, the quoted distance was 200 yards, not feet. Taking the police officer's figure, 0-68mph in 200 yards is 0-60 in 10.9 seconds (and 0-68 in 12.2 seconds), which is an easily attainable figure in a large proportion of modern cars (though it would actually need to be faster than this, since I assumed linear acceleration).

Adding the slope into account, a quick and dirty calculation I just ran indicates that the hill would soak up about 15 horsepower or so on average during such an acceleration run. Honestly, these numbers are making it look like it would be possible for a lot of cars to achieve this performance, though it would involve accelerating fairly briskly (possibly pretty close to floored, for a lot of normal commuter cars).

Last edited: May 18, 2015
11. May 18, 2015

### LaureeF

It's 200 yards, not feet.

12. May 18, 2015

Staff Emeritus
Even that is pushing it. That would require your foot to be on the floor for the whole time.

13. May 18, 2015

### LaureeF

Thank you. You've been a big help. I appreciate it.

14. May 18, 2015

Staff Emeritus
I did goof with feet, but even with yards, it involves flooring it. Apologies for switching to metric: 53mph means 280 J/kg from kinetic energy. A 3 degree hill means a rise of 9.6 m, or 95 J/kg from potential energy (a 33% "tax", if you will). That means, on an equivalent flat surface, the car would go sqrt(4/3) faster, or 61 mph at the end of the 200 yards. That's a 0-60 time of 13.1 seconds.

Edmunds says 11 seconds. While this is possible, it requires a foot pretty much on the floor. That's inconsistent with the "normal acceleration" description. Which is why I think remeasuring is in order.

15. May 18, 2015

### LaureeF

16. May 18, 2015

### LaureeF

Thank you for taking the time to help me. It is truly appreciated.

17. May 18, 2015

### LaureeF

Thank you so much for your help. It was very kind of you.

18. May 18, 2015

Staff Emeritus
Now that I think about it, I think you have given us enough information to refute your position. (Sorry, but that's how it works out). You want to show that with normal acceleration, you got to 53 mph, but that the car mechanically could not reach 68 mph in the same stretch. Is that right?

The key is "normal acceleration". My car can provide 200hp, but under normal acceleration, it's 100 hp or even less. If you can reach 53 with normal acceleration, you can probably reach 68 by flooring it.

19. May 19, 2015

### cjl

Yes, and unfortunately, if the car is physically capable of reaching 68mph in that distance, you can't refute the officer's claim, unless you have a way to conclusively prove that you weren't flooring the accelerator.

20. May 19, 2015