# Thread: Im having issues with integrals

1. ## Im having issues with integrals

Ok, in calculus right now we are working on integrals. I cannot figure out how to do these word questions with velocity and acceleration in them. Can someone please show me how?

1. A car is moving along a straight flat road at a velocity of 90 km/hr. The driver applies the brakes so it decelerates at 10 m/s^2. How long will it take to stop? How far will the car travle from the time the brakes are applied?

2. An object is moving along a streight line with its position messured relitive to a fixed point O. The velocity of the object at any time is v(t)= 3t^2 cm/s. Initaily the object is 8 cm to the left of the point O. Deturmine the objects accseleration when it is at O.

3. A ball is dropped from the 553 m tall CN tower in toronto. What is the velocity of the ball when it hits the ground?

2. ## Re: Im having issues with integrals

1. Set t=0 when the driver applies the brakes. You should be able to write an equation for the speed of the car from t=0 until it stops. Then you integrate to get the distance traveled.

2. You integrate the velocity to get an equation for position, and use 8cm to evaluate the constant of integration. Then you solve to find the time when it's at O. Then you differentiate the velocity to get the acceleration as a function of time and evaluate it at the time you calculated.

3. Here you need the acceleration due to gravity. You can write an equation for the velocity as a function of time, then integrate to get position as a function of time, then set it to 553 to get the time when it hits the ground. Then you plug in to your equation for velocity.

That's an overview of the process - if you're having trouble with a specific step, post again and we'll help you through it.

- Hollywood

3. ## Re: Im having issues with integrals

Im still so confused. I think my main problem is Im unsure of what eqauision to begin with.

4. ## Re: Im having issues with integrals

Then think about it. The velocity is decreasing at a constant rate. What type of a function do you think that would be if the rate is constant?

5. ## Re: Im having issues with integrals

You sound just like my Phisics teacher. He always tells me to think about it and never answers my question. Which just stresses me out, because I AM thinking about it. But I have no idea what im doing in the first place. This unit in calculus is just like phisics, and I have no idea what im doing. I dont know what it means when the rate is constant. All i know about constants is they go in befor you differentiate. But this is doing the opposite of differantiating, and I dont have any eqausion to put anything into. I just have a bunch of random information that I dont know what to do with.

6. ## Re: Im having issues with integrals

Ok, let's try (on #1) to make a graph of velocity vs. time. You have v=90 at t=0, so that's a point at (0,90). The car decelerates at 10m/sec^2, so it goes through (1,80), (2,70), etc. and you have a line segment sloping down to (9,0). You should be able to write an equation for this line segment y = some function of x, where x goes from 0 to 9. So how long does the car take to stop?

If this part is easy for you - hopefully it is - try to continue with the next step on #1, and try to make graphs of velocity vs. time on #2 and #3.

- Hollywood

7. ## Re: Im having issues with integrals

Originally Posted by Twinkie
You sound just like my Phisics teacher. He always tells me to think about it and never answers my question. Which just stresses me out, because I AM thinking about it. But I have no idea what im doing in the first place. This unit in calculus is just like phisics, and I have no idea what im doing. I dont know what it means when the rate is constant. All i know about constants is they go in befor you differentiate. But this is doing the opposite of differantiating, and I dont have any eqausion to put anything into. I just have a bunch of random information that I dont know what to do with.
If you are doing calculus and can not even relate a given rate to a type of function, then you need more help than can be given here, such as private tutoring. Also, why should we take the time to try to explain something to you or to try to get you to understand something if all you are going to do is complain about not having any idea what you are doing? Why haven't you tried a few different problem solving strategies (such as drawing a few graphs, or making a table of numbers, or at least doing SOMETHING which could spark up an idea)?