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**1.2 ****
Speed, distance and time calculations - problem solving**

The speed
(or velocity) of a moving object is rarely constant.

When you walk, run or travel in a car or
train your/their speed
is constantly changing.

The speed that a person can walk, run or cycle
depends on many factors including: age, distance travelled, fitness and terrain.

**Typical values** may be taken as: (maths
reference to put speeds in perspective: 1 hour
≡ 3600 s, 1 mile = 1.61 km)

**You are expected to know typical
values for commonly sited moving objects!**

walking (briskly on the flat?) ̴ 1.5 m/s, ~5400
m/hour, ~5.4 km/hour, ~3.4 mph

You can do a simple experiment to
time a person walking a certain measured distance on the floor.

You multiply **km/hr x 1.6 to
convert to mph**.

**km/hr into m/s**: the factor is
x 1000 for m then divide by 3600 seconds/hr, so **m/s = (km/hr) ÷ 3.6**

running ̴ 3 m/s, ~11000 m/s,
~11 km/hour, ~6.7 mph

Again you can do a simple experiment
to time a running a certain measured distance on a running track.

light wind ~5 m/s, blowing gale ~20 m/s,
hurricane ~50 m/s

cycling ̴ 6 m/s, ~22000 m/s,
~22 km/hour, ~13 mph

A jet aircraft travelling at 600 km/hour
is moving at 168 m/s (from 600 x 1000/3600, 3 s.f.).

A
car travelling at 50.0 mph, speed = 50.0 x 1.61 = 80.5 km/hour, 1000 x 80.5
÷ 3600
= 22.4 m/s

Speed restricted in built up areas 30
mph, 47 km/hr, 13 m/s

Less restricted areas like motorways
with a higher speed limit of
70 mph, 112 km/hr, 31 m/s

A
train travelling at 200 km/hour (~ 124 mph) is moving at a speed
of ~56 m/s.

Sound travels at ~340 m/s (1224 km/hour,
~761 mph), but this varies
with air pressure (density) and temperature.

Sound travels much faster through and
liquids, ~1500 m/s in water, used in ultrasound depth measurement and surveying,

and even faster in solids >3000 m/s (e.g.
earthquake waves, at ~3 km/s you don't get much warning!)

The ultimate speed of anything is that of
'light' photons, all electromagnetic radiation travels at the 'speed of light' which is
greatest in vacuum and is ~3.0 x 10^{5} km/s (~3.0 x 10^{8} m/s,
186,000 miles/s), .

**
The formula for speed/velocity and example
calculations****
- problem solving**

speed (metres/second, m/s) = distance travelled
(metres, m) ÷ time (seconds, s)

distance (m) = average speed (m/s) x time (s)

time (s) = distance (m) ÷ average speed (m/s)

**
v = s****
÷ **
**t**, so **
**s =
**v** x** t**
and **t = s****
÷ **
**v**

**v =** speed or velocity (**m/s**),
**s =**
distance (**m**), t = time (**s**)

sometimes distance is quoted as the
variable d as well as s.

Changes in distance might be called
Δd (or Δs) and changes in time Δt - the actual time taken for the
distance of actual moved in that time.

Make sure you are good at doing
**equation rearrangements**,
this one is easy, but some are not! **
It is better to be able to
rearrange a formula than use a formula triangle.**

Beware! it is common in motion topics to
represent distance by the letter **s**, don't confuse with the time unit
second!

If the speed of an object is variable,
**average speed** is simply the total distance travelled divided by the total time
taken.

e.g. a sprinter completing a 200 m race in 25
seconds has an average speed of 200 / 25 = 8 m/s, but quite plainly the speed is
variable as the athlete starts from 0 m/s to perhaps a maximum speed of over10 m/s
since 100 m sprinters complete their distance in ~10 s giving an average speed
of ~10 m/s.

For** v** to be a velocity, then direction
of motion should be specified.

**Example
of speed calculation questions**

**
Q1.1** A train was timed to take 2.5 seconds when passing between two
posts 100 m apart.

(a) What is the speed of the train in
m/s?

(b) What is the speed of the train in
km/hour?

(I'm just deliberately asking a more
arithmetically awkward question of a sort you may have to deal with)

Worked out ANSWERS for these speed calculation questions

Q1.2 How far will a car travel in 15 seconds at a speed of 20 m/s?

Worked out ANSWERS for these speed calculation questions

**
Q1.3** A sprinter runs 400
m at an average speed of 8.4 m/s. To the nearest 0.1 s, how long did the sprint
run take?

Worked out ANSWERS for these speed calculation questions

**Q1.4**
A car travels at a constant speed of 40.0 mph.

(a) If 1 mile = 1.61 km, calculate the
speed of the car in m/s.

(b) How far will the car travel in 45.0
seconds?

(c) If the car speeds up and travels 5.2
km in 3 minutes, what is the car's speed?

Worked out ANSWERS for these speed calculation questions

**Q1.5**
A car travels from motorway Junction 26 to Junction 27 with an average speed of
30 m/s (~67 mph).

It took 150 s to go from Junction 26 to
Junction 27.

Due to road works speed restrictions the
car moved on to Junction 28 at average speed of 20 m/s.

Junctions 27 and 28 are 15 km apart.

**(a) Calculate how far apart Junctions
26 and 27 are.**

**(b) Calculate how long it took to
travel between Junctions 27 and 28.**

**(c) What is the average speed of the
car from Junction 26 to Junction 28?**

Worked out ANSWERS for these speed calculation questions

INDEX physics notes: Speed
calculations and distance-time
graphs

**
Keywords, phrases and learning objectives for****
speed, motion and graphs**

Know the formula for speed and be able to do various
examples of speed, distance and time calculations.

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INDEX physics notes: Speed
calculations and distance-time
graphs