Acceleration

Acceleration is the change of the speed per second      (if the speed is in m/2)
Take 2 points, perhaps t=0 and t=1
then you can use $a=\frac{∆v}{∆t}=\frac{37,5-22,5}{1}=15$

But in c they are asking specifically about the acceleration at 0.5 seconds . Why is it wrong to calculate it in this way : 

(0-30)/(0-0.5)=60m/s^2

It's wrong because you enter a spesific time and use corresponding speed. What if you wanted the acceleration for t=0?
You do see that the acceleration is the same for t=0, t=0,5,t=1 but something else for t=1,5, t=2 etc, right?

So, you draw a tangent to the curve at 0,5 and use that. But since the line is the same from t=0 to t=1 you can use that as your tangent.

It means  that  the acceleration is the same when t=0.5 , or t=1 . If I choose forexample t=0 v=37.5 

and t=0.5 v=30 I could calculate the acceleration using the formula 

(v1-v2)/(t1-t2)=(37.5-30)/(0-0.5)=-15m/s^2