9.2 Speed & Simple Calculations

9.2 Speed & Simple Calculations

Speed tells you how much distance something covers in a given time. ICAS Paper E expects you to calculate speed — and even acceleration — from given formulas, and the good news is the formulas are always given in the question. Your job is to put the right numbers in the right places.

The Speed Formula

speed = distance ÷ time

If a toy car rolls 6 metres in 3 seconds, its speed is 6 ÷ 3 = 2 metres per second (m/s). The unit comes straight out of the calculation: metres divided by seconds gives m/s. For bigger journeys we use kilometres per hour (km/h): a bus that covers 90 km in 2 hours travels at 90 ÷ 2 = 45 km/h.

The one formula rearranges into three, and ICAS uses all three forms:

• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed

Many students remember them with a formula triangle: write distance on top with speed and time underneath, cover the quantity you want, and what remains shows the calculation. Cover distance and speed sits beside time, so multiply. Cover speed and distance sits over time, so divide.

Worked example, fun-run style: Asha runs the 2 km school fun-run. Her first kilometre takes 6 minutes and her second takes 9 minutes — a total of 15 minutes. Her average speed for the whole run is 2 km ÷ 0.25 h = 8 km/h. Notice the trap: 15 minutes is a quarter of an hour, so you must convert before dividing — 2 ÷ 15 would mix kilometres with minutes and give a nonsense unit. Always check that the units in the question match the units in your answer.

Worked Example: Toy Car Down a Ramp

A class rolls a toy car down a ramp and times it with a stopwatch. The car covers 1.5 metres in 3 seconds, so its speed is 1.5 ÷ 3 = 0.5 m/s. The students then prop the ramp up steeper, and the same car now covers the same 1.5 metres in 2 seconds — a speed of 1.5 ÷ 2 = 0.75 m/s. The steeper ramp lets gravity pull the car more effectively along the slope, so the unbalanced force is bigger and the car accelerates more. These figures are average speeds over the whole run, because the car starts slowly and speeds up as it rolls. If a question asks why the second run was faster, the answer links straight back to Section 9.1: a steeper ramp means a bigger net force down the slope, and friction stays much the same.

One last unit skill: to convert m/s into km/h, multiply by 3.6 (because there are 3,600 seconds in an hour and 1,000 metres in a kilometre). A sprinter at 10 m/s is travelling at 36 km/h — faster than most suburban traffic.

Average Speed vs Instant Speed

Asha did not run every metre at the same pace — she started fast and tired later. Her average speed is the total distance divided by the total time, smoothing over all the speeding up and slowing down. Her instantaneous speed is how fast she was going at one particular moment — what a car's speedometer shows. When an ICAS question gives a journey broken into stages, it is almost always asking for average speed over the whole journey: add up all the distance, add up all the time, then divide. Do not just average the stage speeds unless every stage took the same amount of time.

Reading Distance–Time Graphs

A distance–time graph puts time on the horizontal axis and distance travelled on the vertical axis. Three shapes cover nearly every question:

A changing slope tells a story: steep, then flat, then gentle means fast, then stopped, then slow. A curve that gets steeper shows speeding up; a curve that flattens shows slowing down. And because steepness is distance divided by time, the slope of a distance–time graph is the speed.

Acceleration (Paper E)

Acceleration is how quickly speed changes. The given formula is:

acceleration = change in speed ÷ time taken

A cyclist goes from 4 m/s to 10 m/s in 3 seconds. The change in speed is 10 − 4 = 6 m/s, so the acceleration is 6 ÷ 3 = 2 metres per second squared (m/s²). Slowing down is acceleration too — a negative one, sometimes called deceleration. Keep it simple: subtract the starting speed from the final speed, divide by the time, and state the unit.

Comparing from a Table

ICAS often hides the same skill inside a results table. Two cyclists each ride 100 m: Beth takes 25 s and Chen takes 20 s. Beth's speed is 100 ÷ 25 = 4 m/s; Chen's is 100 ÷ 20 = 5 m/s, so Chen is faster. When distances are equal, the shorter time always wins — you can sometimes answer without finishing the arithmetic, but be ready to show the calculation when the question asks for an actual speed.