Speed, Distance and Time

طریقہ، مرحلہ وار

1. 1

   Start from speed = distance ÷ time

   150 km in 2 hours → 75 km/h

   The unit itself states the formula: kilometres per hour means kilometres divided by hours. Reading the unit is a reliable way to reconstruct the relationship without relying on a remembered triangle.

2. 2

   Rearrange for whichever is unknown

   distance = speed × time · time = distance ÷ speed

   These are the same relationship written three ways. Students who understand it as rearrangement rather than three formulas can also handle density and pressure, which behave identically.

3. 3

   Convert units before substituting

   45 minutes = 0.75 hours, not 0.45

   Time in minutes must become hours before use with km/h. Writing 45 minutes as 0.45 hours is the single most frequent error in the topic, and it produces an answer that looks entirely plausible.

4. 4

   Average speed uses totals, not an average of speeds

   total distance ÷ total time

   For a journey of 60 km at 60 km/h then 60 km at 30 km/h, the average is 120 ÷ 3 = 40 km/h, not 45. Averaging the two speeds ignores that more time was spent at the slower one.

5. 5

   Read gradients on a distance-time graph

   steeper line → faster. horizontal line → stationary

   The gradient of a distance-time graph is speed, because it is change in distance over change in time. A horizontal section means distance is not changing, so the object has stopped.

Units cause most of the errors

The arithmetic in this topic is straightforward and the units are not. Minutes must be converted to hours, metres to kilometres, and a speed in m/s cannot be used with a distance in kilometres without conversion. Almost every wrong answer traces to a unit that was not converted.

Writing the units alongside every number, and cancelling them as the calculation proceeds, catches these immediately. If the units of the answer come out as km·min/h, something was not converted.

• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
• 45 minutes = 0.75 hours
• Average speed = total distance ÷ total time

Average speed is not the average of the speeds

This is the topic's most reliable trap. Travelling out at 60 km/h and back at 30 km/h over the same distance does not average 45 km/h, because the slower leg takes twice as long — so more of the journey is spent at 30.

The only safe method is total distance divided by total time. Working out each leg's time separately and adding them makes this mechanical, and it is worth doing even when the shortcut looks tempting.

What the graph shows

On a distance-time graph the gradient is the speed. A steeper line means faster travel, a horizontal line means stationary, and a line returning towards the axis means travelling back towards the start.

Speed-time graphs behave differently: there the gradient is acceleration and the area under the line is the distance travelled. Confusing the two graph types is common and the axis labels are the only reliable way to tell them apart.

How we teach speed, distance and time

We teach the relationship as one formula rearranged rather than as a triangle to memorise. The triangle works until a student meets density or pressure, at which point they need another triangle; rearranging works for all of them.

We convert units as a separate written line before any substitution. It looks like extra work and it is where the marks are, particularly on the minutes-to-hours conversion that catches so many otherwise correct answers.