Guide To Calculations In Science

• Read the question. Do you understand what the question is asking, and the format of answer required?

A ball is dropped from rest and falls 5 m to the ground. What is the speed of the ball just before it hits the ground?

• Draw the diagram. Questions rarely have a single `THE force` c. - drawing and labelling the diagram of what is happening will help you see what is what. It doesn`t have to be pretty, but it should be easy to read, so make it reasonably large.
• What do I already know? Make a list of the relevant information from the question and from general knowledge. For instance for questions about motion, I write out the suvat properties e.g.

s = 5 m

u = 0 (ball starts from rest)

v = ? <- WANT TO FIND THIS

a = 10 m/s² (gravity, +ve = downwards)

t = ? I don`t need to find it.

• What equation includes the things I know and the things I want to find?

For this question, we want v² - u² = 2as

• Rearrange the equation before putting numbers in - it saves time and avoids using rounded-off numbers.

u=0 so we can simplify to v² = 2as

v = (2as)

• Put in the numbers to find the answer.

v = (2 x 10 x 5)

= 10 m/s

• Is this a sensible answer? Compare with other numbers in the question or with familiar objects. Check the units are right (if they aren`t, there must be a problem with the equation).

Acceleration is in m/s², times distance in m, giving m²/s². We square-root this to get m/s, which is the right unit for a speed.

The ball speeds up by 10 m/s for every second it falls. A ball falling 5 m (e.g. dropped from an upstairs window) might take a second to hit the ground. So 10 m/s seems about right.

A hiker with a backpack might walk at 4 km/h (that was our estimate for Duke of Edinburgh`s Award expeditions), which is 4 x 1600 m / (60 x 60) s = 1.8 m/s or so. I would expect a falling ball to reach several times my walking pace. so 10 seems about right. I would be suspicious if it reached 1 m/s or 100 m/s (which would be about 1/3 of the speed of sound!).

• If there is more than one answer, which of them is correct?

A final speed of -10 m/s would also fit the equation. But if downward movement is positive, this would mean the ball was moving upwards just before it hits the ground, which would be silly. So we can reject the negative answer.