Basic problem in Mechanics

Question

A body starts from rest and builds up to a velocity of 7.2km/hr in half a minute.

A) What is the acceleration? B) What distance is travelled in the half minute?

Apparently the answer is $1/15 m/s^2$ for part A, I've tried used the equation $v = u + at$ but for some reason I keep receiving the answer $240m/s^2$. What on earth am I doing wrong?

Answer 1

You need to do the conversion first. For distance: $$7.2 \text{ km}\times\frac{1000\text{ meters}}{1\text{ km}}=7200\text{ meters}$$ For time: $$1\text{ hour}\times\frac{3600\text{ seconds}}{1\text{ hour}}=3600\text{ seconds}$$ This is then $$\frac{7200\text{ meters}}{3600\text{ seconds}}=2\text{ m}/\text{s}$$ Now use the kinematic equation $$v_f=v_0+at$$ Re-arrange to get $$a=\frac{v_f-v_0}{t}$$ and solve for the acceleration (You know that $t=30\text{ seconds}$). Distance traveled can be found by $$x=v_0t+\frac{1}{2}at^2$$ Having the body start from rest ($v_0=0$) simplifies these a lot.

Answer 2

Sure, I can elaborate. you have $\frac{7.2km}{1hour}$ Convert the top part to meters and the bottom part to seconds. $\frac{7.2 \times 1000}{1 \times 60 \times 60}$ That is how mfl got $2m/s$ above. So now you have an initial velocity of 0. A final velocity of 2. And it had 30 seconds to make the increase.

Answer 3

It looks as though you're not properly converting your units. I think that the easiest way to do this problem is to convert your velocity to meters per second, and your time to seconds. In the comments below your question, mlf provided a formula to convert the units of velocity from $\text{km/h}$ to $\text{m/s}$. I'll explain how mlf came to that formula. There are 60 seconds in a minute, and 60 minutes in an hour. Therefore, $1\,\text{h} = 60*60 \,\text{s} = 3600 \,\text{s}$. Similarly, there are 1000 meters in a kilometer, so $1 \,\text{km} = 1000 \,\text{m}$. Combining these conversion factors, we get:

$1 \, \text{km/h} = (1000 \, \text{m})\left(\frac{1}{ 3600 \, \text{s} }\right) = \frac{5}{18} \,\text{m/s}$.

If we multiply both sides of this equation by 7.2, we can convert 7.2 $\text{km/h}$ to meters per second:

$7.2 \, \text{km/h} = (\frac{5}{18}\times 7.2) \,\text{m/s} = 2.0 \,\text{m/s}$.

Now that we've converted our velocity from kilometers per hour into meters per second, we can convert our change in time to seconds. Half a minute corresponds to $30 \, \text{s}$, so the time-value is $30 \, \text{s}$. From here, all that's left to do is plug our velocity and change in time values into the equation $a = \frac{\Delta v}{\Delta t} $, where $\Delta v$ represents the change in velocity, and $\Delta t$ represents the change in time Do so and you'll get the desired answer.

Hope this helps!