Uniform Rectilinear Motion

Lessons

Senior 1 · Physics

Uniform Rectilinear Motion

5 lessons

Lesson 5 of 5

Uniform Motion in Everyday Life

25 min

Flash, then bang

During a storm over Kigali you see a flash of lightning, then count: one, two, three, four, five, six... and the thunder rolls. The lightning and the thunder happened at the same moment, so why do you hear it six seconds late? Light reaches you almost instantly, but sound is slow: it crosses the distance at a steady speed of about $340\,\mathrm{m\,s^{-1}}$ . Six seconds of travel at that speed means the storm is about 2 km away. The simple equation of uniform motion, $d = v t$ , has just told you how far off the danger is.

Definition

The speed of sound in air is about $340\,\mathrm{m\,s^{-1}}$ ; it changes a little with temperature. The speed of light is $3.0 \times 10^{8}\,\mathrm{m\,s^{-1}}$ , so fast that light from a flash a few kilometres away arrives in about a hundred-thousandth of a second.

An echo is a sound reflected back from a large surface such as a wall or a cliff.

Experiment: the speed of sound by echoes

Figure 5.1: The echo method. Each clap travels to the wall and back, 170 m in total, before the next clap.

Find a large, flat wall with open ground in front of it. Measure 85 m from the wall with a long tape measure.
The clapper claps two blocks of wood together, then keeps clapping so that each clap is made at the same moment as the echo of the one before is heard.
When the rhythm is steady, the timekeeper times 20 intervals between claps. Repeat three times.

Trial	1	2	3	Mean
Time for 20 intervals (s)	10.2	9.9	10.0	10.03

One interval is $\frac{10.03\,\mathrm{s}}{20} = 0.50\,\mathrm{s}$ , in which the sound travels 170 m, so

v = \frac{d}{t} = \frac{170\,\mathrm{m}}{0.50\,\mathrm{s}} = 340\,\mathrm{m\,s^{-1}}

Important

Safety. Choose a place away from roads and traffic. Never do this experiment, or any outdoor activity, while a thunderstorm is close.

Worked example 1: how far away is the lightning?

Thunder is heard 6.0 s after a flash. How far away was the lightning? (Speed of sound $= 340\,\mathrm{m\,s^{-1}}$ .)

The light arrives almost at once, so the 6.0 s is the travel time of the sound.

d = v\,t = 340\,\mathrm{m\,s^{-1}} \times 6.0\,\mathrm{s} = 2040\,\mathrm{m} \approx 2.0\,\mathrm{km}

A quick rule: every 3 seconds of counting is about 1 km.

Important

Lightning safety. Lightning kills people in Rwanda every year, especially during the rainy seasons. If you hear thunder less than 30 s after the flash, the storm is within about 10 km and you can be struck: go inside a building (not under a tree) and stay there until 30 minutes after the last thunder.

Thinking distance on the road

When a driver sees danger, there is a delay, the reaction time, before the foot reaches the brake. During that time the vehicle keeps moving at its full speed: uniform motion. The distance covered is the thinking distance:

d_{\text{thinking}} = v \times t_{\text{reaction}}

An alert driver reacts in about 0.7 s. Tiredness, alcohol or looking at a phone can make it two or three times longer. The brakes then need extra distance, the braking distance, to stop the vehicle.

Worked example 2: a moto's thinking distance

A moto rider travelling at $15\,\mathrm{m\,s^{-1}}$ (54 km per hour) has a reaction time of 0.70 s. How far does the moto travel before the brakes are even touched?

d = v\,t = 15\,\mathrm{m\,s^{-1}} \times 0.70\,\mathrm{s} = 10.5\,\mathrm{m}

If the rider is reading a phone message and takes 1.5 s to react, $d = 15 \times 1.5 = 22.5\,\mathrm{m}$ : more than twice as far, before braking begins.

When will they meet?

Two vehicles moving towards each other along the same road close the gap between them at the SUM of their speeds. Draw both journeys on one position–time graph: the point where the lines cross is where and when they meet.

Figure 5.2: Position against time. The bus starts at Kigali (0 km) and the car at Muhanga (50 km); the lines cross after 0.50 h, 30 km from Kigali.

Worked example 3: Kigali and Muhanga

Kigali and Muhanga are about 50 km apart by road. At 8:00 a bus leaves Kigali for Muhanga at a steady $60\,\mathrm{km\,h^{-1}}$ , and a car leaves Muhanga for Kigali at a steady $40\,\mathrm{km\,h^{-1}}$ . When and where do they meet?

Together they close the gap at $60 + 40 = 100\,\mathrm{km\,h^{-1}}$ , so

t = \frac{d}{v} = \frac{50\,\mathrm{km}}{100\,\mathrm{km\,h^{-1}}} = 0.50\,\mathrm{h}

They meet at 8:30. In that time the bus has gone $x = 60 \times 0.50 = 30\,\mathrm{km}$ from Kigali. Check with the car: it has gone $40 \times 0.50 = 20\,\mathrm{km}$ from Muhanga, and $30 + 20 = 50\,\mathrm{km}$ .

Warning

Keep the units consistent. Use kilometres with hours, or metres with seconds, never a mixture. A reaction time is usually given in seconds, so change the speed to $\mathrm{m\,s^{-1}}$ first: $54\,\mathrm{km\,h^{-1}} = 15\,\mathrm{m\,s^{-1}}$ .

Tip

For every uniform-motion problem, write down the three quantities $d$ , $v$ and $t$ , mark the one you want, check that the units match, then use $d = v t$ in whichever form you need.

Arrive safely

Rwanda National Police's road safety campaign, Gerayo Amahoro ("arrive safely"), reminds drivers, riders and pedestrians of rules that are pure physics: keep to the speed limit, keep a safe distance behind the vehicle in front, and never use a phone while driving. Each rule shortens the distance a vehicle travels before it can stop.

Stopping Distance (FuseSchool). Watch for the two parts of stopping distance, thinking distance and braking distance, and what makes each one longer.

✦

Practice

Thunder is heard 9.0 s after a flash of lightning. How far away is the storm? (Speed of sound $= 340\,\mathrm{m\,s^{-1}}$ .)
A pupil stands 170 m from a cliff and shouts. How long after the shout does she hear the echo?
A car travels at $72\,\mathrm{km\,h^{-1}}$ . Its driver's reaction time is 0.60 s. Find the thinking distance.
Two cyclists start 12 km apart and ride towards each other along a straight road at $14\,\mathrm{km\,h^{-1}}$ and $10\,\mathrm{km\,h^{-1}}$ . After how many minutes do they meet?
A bus leaves a town at 9:00 at $50\,\mathrm{km\,h^{-1}}$ . A car leaves the same town at 10:00 on the same road at $75\,\mathrm{km\,h^{-1}}$ . At what time does the car catch up with the bus?
Why does a driver who is using a phone need a longer distance to stop, even though the brakes are just as good?
In the echo experiment, a class uses a wall only 20 m away. Explain why their result for the speed of sound is likely to be poor.

Show answersHide answers

$d = 340 \times 9.0 = 3060\,\mathrm{m} \approx 3.1\,\mathrm{km}$
The sound travels $2 \times 170 = 340\,\mathrm{m}$ : $t = \frac{340}{340} = 1.0\,\mathrm{s}$ .
$v = 72 \div 3.6 = 20\,\mathrm{m\,s^{-1}}$ ; $d = 20 \times 0.60 = 12\,\mathrm{m}$
Closing speed $14 + 10 = 24\,\mathrm{km\,h^{-1}}$ ; $t = \frac{12}{24} = 0.50\,\mathrm{h} = 30\,\mathrm{min}$ .
At 10:00 the bus is 50 km ahead. The car gains $75 - 50 = 25\,\mathrm{km\,h^{-1}}$ , so it needs $\frac{50}{25} = 2.0\,\mathrm{h}$ : it catches up at 12:00, 150 km from the town.
The phone lengthens the reaction time. During the reaction time the vehicle keeps moving at full speed, so the thinking distance, and therefore the total stopping distance, is longer.
The echo would return after only $\frac{40}{340} \approx 0.12\,\mathrm{s}$ , which is less than a person's reaction time and too short to clap and time accurately. A longer distance gives a longer, more measurable time.

Key points

Many everyday problems are uniform motion: use $d = v t$ with consistent units.
Sound travels at about $340\,\mathrm{m\,s^{-1}}$ in air: every 3 s between flash and thunder is about 1 km.
Thinking distance = speed $\times$ reaction time; anything that slows your reaction makes it longer.
Objects moving towards each other close the gap at the sum of their speeds; on a position–time graph they meet where the lines cross.

1Flash, then bang

2Experiment: the speed of sound by echoes

3Thinking distance on the road

4When will they meet?

5Arrive safely

Flash, then bang

Experiment: the speed of sound by echoes

Thinking distance on the road

When will they meet?

Arrive safely