# First derivative problem

Danatron
A Car, initially traveling at the speed 100 km/h, slows down according to the formula. L(t)= At - Bt^2
Where L is the traveled 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:

Gold Member
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?

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.

Gold Member
The car has a velocity of 100km/h and slows down to 10km/h?
Yes. You can think of the situation as the car applying brakes and decelerating at a constant rate.

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

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