Calculating Maximum Acceleration in a Utility Vehicle with Additional Mass

[Khang]

[Mentor's Note: Thread moved to Introductory Homework Forum]
What's up.
I have this question in my physics book regarding what forces do.
Can I please get help with this question.

A utility vehicle has a maximum acceleration of 6.0 m/s when it carries only the driver and has a total mass of 5000 kg. What is it's maximum acceleration after picking up six passengers and their luggage, adding an additional 800 kg mass?

Basically, my maths is a bit rusty, so I thought I would write it like 800/5000 X 6.0, which gave me 0.96, obviously wrong. The answer is 5.2 m/s, which just seemed odd to me. Keep in my mind, they haven't introduced Newtons second law in the book yet. All I know is that acceleration is inversely proprortional to mass.

Also, can anyone explain why we put squared inddicie next to the seconds in m/s. I suck at maths and Physics so badly, so please forgive me if this is an extremely dumb thread.
Yes, I am an undergraduate who has never done much physics before.

 

[Orodruin]

A utility vehicle has a maximum acceleration of 6.0 m/s

This cannot be true, acceleration is measured in length/time^2 and so m/s is not a valid unit for acceleration (see below). For the rest, I will assume that you mean 6 m/s^2.

What is it's maximum acceleration after picking up six passengers and their luggage, adding an additional 800 kg mass?

Are you familiar with Newton's second law?

Also, can anyone explain why we put squared inddicie next to the seconds in m/s. I suck at maths and Physics so badly, so please forgive me if this is an extremely dumb thread.

Acceleration describes how much velocity changes with time. If you want to describe this, the quantity you are computing is a change in velocity divided by the time it took to change the velocity (to be accurate, you do this in the limit of small times): a = dv/dt. The dimensions of velocity is length/time and describes how far something moves in a given time (again, in the small time limit) and the dimension of time is time (surprise!). This means that if you divide a velocity by a time, you end up with something which has dimensions of [dimension of velocity]/[dimension of time] = (length/time)/time = length/time^2.

 

[Khang]

Thanks for your explanation about the ^2!
I'm slightly familiar with Newton's law. But all they are telling us is that mass is inversely proportional to acceleration, and force is directly proportional to acceleration, and we have to use that.
I don't think I'm supposed to use Newtons law for it. I need the force to do that right? I don't see how I can get the force for it with only the mass. In another question similar to this, they only give us acceleration, not the mass or anything else. They gave one example of finding the mass, which I reversed to finding the acceleration (I added that in my question) and that didn't work.

 

[Orodruin]

You have the mass and acceleration for the unloaded case, which tells you how much force the vehicle will be able to supply. The underlying assumption is that the maximal force does not change with the load.

 

[Khang]

Thank you, that was a great help! I went 5000 x 6.0 which gave me 30000 units. Then I went a = 30, 000 divided by 5800 which gave me 5.17, so they must have rounded it off to just two.

Yet, it perplexes me still. I used this for another question; which is

A truck has a maximum acceleration of 10.0m/s. What will the maximum acceleration be if the truck is towing a car whose mass is half that of the truck?

There is no given mass, so I made up my own, 5000 Kg X 10 = 50 000 N, 50 000/7500, and I got 6.7 rounded off, which according to the book is the right answer. But I don't understand how, and I didn't much for the first question I posted. Because if we double the mass, 10 000, the acceleration should be 5.0 m/s, because it's inversely proportional. So then this led me to think that the maximum acceleration of the truck towing a car half it's size would be 7.5 m/s^2. So yeah, ...I, a very bad person at maths, am skeptical about this mathematical logic.

 

[CWatters]

A utility vehicle has a maximum acceleration of 6.0 m/s when it carries only the driver and has a total mass of 5000 kg. What is it's maximum acceleration after picking up six passengers and their luggage, adding an additional 800 kg mass?

Basically, my maths is a bit rusty, so I thought I would write it like 800/5000 X 6.0, which gave me 0.96, obviously wrong. The answer is 5.2 m/s, which just seemed odd to me. Keep in my mind, they haven't introduced Newtons second law in the book yet. All I know is that acceleration is inversely proportional to mass.

Ok so sticking with the bit in red and ignoring Newton which hasn't been covered yet..

What you could have done is write out the bit in red as

Acceleration = constant / mass

Then write two versions of that..

6.0 = constant / 5000
Anew = constant/ 5800

Substitute to eliminate the constant of proportionality and you get

Anew = 6.0 * 5000 / 5800 = 5.2m/S²

 

[CWatters]

A truck has a maximum acceleration of 10.0m/s. What will the maximum acceleration be if the truck is towing a car whose mass is half that of the truck?

Do it the same way...

10 = constant/mass
Anew = constant/(1.5 * mass)

Substitute to eliminate the constant and the mass..

Anew = 10/1.5 = 6.7 m/S²