How Do You Calculate the Moment When Speed Changes in a Decelerating Car?

  • Thread starter Danatron
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In summary: So you can take the first derivative of L(t) to get the velocity function, set it equal to 10 and solve for t. This will give you the time moment when the car's speed becomes 10 km/h. Then, you can take the second derivative of L(t) and plug in the value of t to get the acceleration at that moment. In summary, using calculus, you can find the time moment when the car's speed becomes 10 km/h and the acceleration of the car at that moment.
  • #1
Danatron
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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
 
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  • #2
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
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
Danatron said:
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.
 
  • #5
Do you know where i could do some reading to find out where to begin with this problem?
 
  • #6
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
If you know calculus, then the first derivative of distance is velocity, and the second derivative is acceleration.
 

1. What is a first derivative problem?

A first derivative problem refers to a mathematical problem that involves finding the rate of change of a function at a specific point. This is done by calculating the first derivative of the function, which represents the slope of the tangent line to the function at that point.

2. How do you find the first derivative of a function?

To find the first derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule, depending on the form of the function. These rules involve taking the derivative of each term in the function and combining them according to the rule. Alternatively, you can also use a calculator or computer software to find the derivative numerically.

3. What is the significance of the first derivative in a problem?

The first derivative of a function represents the instantaneous rate of change of the function at a specific point. This can be interpreted as the slope of the tangent line to the function at that point. It can also indicate the direction of change of the function, whether it is increasing or decreasing, and the concavity of the function.

4. How can the first derivative be applied in real-world situations?

The first derivative has various applications in real-world situations, such as calculating velocity and acceleration in physics, determining the growth rate of populations in biology, and finding the rate of change of stock prices in economics. It can also be used to optimize functions in engineering and business.

5. What are some common mistakes to avoid when solving a first derivative problem?

Some common mistakes to avoid when solving a first derivative problem include forgetting to apply the chain rule when necessary, mixing up the rules for finding derivatives, and making calculation errors. It is also important to pay attention to the units and interpretations of the derivative in real-world applications.

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