How to arrive at answer for integration question

[Alexenn]

Firstly, I am sorry if this is the wrong section (I really didn't know what each section meant, but I posted here since I am beginner)

Homework Statement

A stone is thrown up into the air at 20m/s is accelerated constantly downwards by gravity at about 10m/s²

Find the anti derivative of the acceleration

Note: I am not solving for C

Homework Equations

The Attempt at a Solution

The antiderivative of 20m/s is 10m/s²
and the antiderivate of -10m/s is -5m/s²

Neither of those match up to the answer, so I'm not sure how to arrive at the answer.

The answer in the book is v= -10t + c

Thankyou

 

[JHamm]

If you have $a = 10$ then you need to find $\int 10\ dt$. There's no need to include units in your integral.

 

[Alexenn]

Ah, thank you very much. Can finally get on with work! =)

 

[SammyS]

If you have $a = 10$ then you need to find $\int 10\ dt$. There's no need to include units in your integral.

That should be $a = -10$. Of course, the units are m/s² .

 

[asteriatic]

for your question. As a scientist, my approach to solving this problem would be to use the fundamental principles of calculus. In this case, we are looking for the anti-derivative of the acceleration, which represents the velocity of the stone at any given time. The formula for acceleration is a=dv/dt, where v is the velocity and t is the time. This means that the anti-derivative of the acceleration is the velocity itself.

To find the anti-derivative, we need to integrate the acceleration function with respect to time. In this case, we have a constant acceleration of -10m/s2, which means that the velocity is changing at a constant rate. This can be represented by the equation v= -10t + c, where c is the constant of integration.

To arrive at this answer, we simply need to integrate the acceleration function with respect to time. This can be done by using the power rule of integration, which states that the integral of x^n is (x^(n+1))/(n+1). In this case, the integral of -10 is -10t, and since we are not solving for c, we can leave it as +c.

I hope this explanation helps in understanding how to arrive at the answer for this integration question. It is important to understand the fundamental principles of calculus and how to apply them in solving problems. Keep practicing and seeking help when needed, and you will become more confident in solving these types of problems. Good luck!