Not quite understanding m/s^2

[freeofwork]

Homework Statement

Suppose a car starts from rest. The car accelerates straight
down the road and and at t =30 seconds, attains a speed of
v=30 km/h. Determine the average acceleration of the car.

Homework Equations

a=v_f-v_i/t_f-t_i

The Attempt at a Solution

so the answer is 1000m / hr /s²...
now the textbook wants you to convert it fully into m/s². what would i do next

 

[Doc Al]

so the answer is 1000m / hr /s²...

No, that would be 1000 m/hr/s.

But better to start by converting the speed from km/h to m/s and redoing the calculation. How many seconds in an hour?

 

[EWH]

Convert hours to seconds. I'd have converted 30km/hr to m/s before starting the problem.

You still need to do it by hand to learn it, but when doing such calculations lately I use http://futureboy.us/frinkdocs/" , which can cope with any units automatically. (It also has a web and a smartphone interface. Just be sure to use lots of parentheses, especially in denominators, as 10m/30s =1/3m*s, while 10m/(30s) = 1/3m/s.) It can cope with virtually any units from Irish cubits to crocodiles, and has many cool features that make it easy to use. It's also great for checking your work.

the problem is equivalent to (30km/hr)/(30s) = (30(1000m)/(3600s))/(30s) = (25/3 m/s)/(30s).

 

[cupid.callin]

If you want to be quick in calculations the i will suggest you to stop using calculators and do calculations by hand.

and Doc AL is right ... you problem is just that you need to convert units before you start with the solution ... you can also do it in the end but its easier to do it in beginning.

 

[rwisz]

First, we need to convert the units of speed from kilometers per hour (km/h) to meters per second (m/s). To do this, we can use the conversion factor 1 km/h = 0.2778 m/s. So the speed of the car at t=30 seconds is 30 km/h x 0.2778 m/s = 8.33 m/s.

Next, we can plug in the values into the equation for average acceleration: a = (8.33 m/s - 0 m/s) / (30 s - 0 s) = 0.2778 m/s^2.

This is the average acceleration of the car during the time interval of 0-30 seconds. If we want to convert it to m/s^2, we can simply write it as 0.2778 m/s^2. This means that for every second the car is accelerating, its speed increases by 0.2778 meters per second.