# First derivative problem

1. Jun 4, 2014

### Danatron

A Car, initially travelling at the speed 100 km/h, slows down according to the formula. L(t)= At - Bt^2
Where L is the travelled distance, t is the time & B= 90 km/h^2. Using derivative, find the time moment when the car speed becomes 10 km/h. Find the acceleration of the car at this moment.

i think this is a function (my interpretation below)

50(t)= 100t - 90t^2

would i just have to graph the function?

any guidance appreciated

Last edited: Jun 4, 2014
2. Jun 4, 2014

### CAF123

That formula for L(t) is reminiscent of a constant acceleration motion. So you can find the negative acceleration of the car by inspection (since you know B).

Why is there a 50t on the LHS of your equation?

What definitions of velocity and acceleration do you have? In particular, ones relating to position?

3. Jun 4, 2014

### Danatron

The car has a velocity of 100km/h and slows down to 10km/h?

The 50 was just a random distance number. Disregard it.

4. Jun 4, 2014

### CAF123

Yes. You can think of the situation as the car applying brakes and decelerating at a constant rate.

5. Jun 4, 2014

### Danatron

Do you know where i could do some reading to find out where to begin with this problem?

6. Jun 4, 2014

### CAF123

Do you have an introductory physics textbook? E.g see the first few chapters of Halliday, Resnick, Walker.

Related links:
Section 1 and 3.1 of http://en.wikipedia.org/wiki/Acceleration

If you want to understand things well though, nothing beats a good textbook and the accompanying problems.

7. Jun 4, 2014

### cosmosmike

If you know calculus, then the first derivative of distance is velocity, and the second derivative is acceleration.

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