I need help with this problem:

Question

I need help with this problem:

A car traveling at 43 ft/sec decelerates at a constant 5 ft per second squared. How many feet does the car travel before coming to a complete stop?

I'm not sure where to start, i know how to find antiDerivatives, but i don't even know the equation...

V = dx/dt = 43 - 5 t
Integral of dx = distance travelled = X
X = Integral of Vo - at = (43 - 5t) dt from t = 0 until the time it takes to stop.

The time it takes to stop is Vo/a = 43/5 = 8.6 s

X = Vo^2/a - (1/2)*a*(Vo/a)^2
X = (1/2) Vo^2/a

This formula is often used in physics, but here I have assumed you wanted a mathematical derivation

thanks! perfect!

i need the anti derivative of 2x/x^2 thanks.

Answer 1

The car is travelling 43ft/sec and decelerating at 5ft/s so we can assume it takes 43/5 seconds to stop. The car is slowing down constantly so the average speed of the car can be determined by 43/2 and then multiplying by the time it takes to stop the car we can find how many feet the car traveled before it stopped. (43/2 times 43/5 = 184.9 ft.)

Answer 2

To find the antiderivative of the function 2x/x^2, you can use the power rule for integrals.

The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.

In this case, we have 2x/x^2, which can be simplified as 2/x.

Using the power rule, the antiderivative of 2/x is 2 * (x^(1-1)) / (1-1+1), which simplifies to 2ln|x| + C.

Therefore, the antiderivative of 2x/x^2 is 2ln|x| + C.

Answer 3

To find the antiderivative of the function f(x) = 2x/x^2, you can use the properties of logarithms. The general form for the antiderivative of a function f(x) = k/x is ln|x| + C, where k is a constant and C is the constant of integration.

Let's apply this property to our function f(x) = 2x/x^2:

First, we simplify the function by canceling out a common factor of x from the numerator and denominator:
f(x) = 2/x

Now we can use the property mentioned earlier:
∫(2/x) dx = 2∫(1/x) dx = 2 ln|x| + C

So the antiderivative of the function f(x) = 2x/x^2 is 2 ln|x| + C, where C is the constant of integration.