SPEED, DISTANCE & TIME
Suppose
you always go to college on the bike which is 5 km away from your home you
might hear from your mom/dad that drive slowly or don’t increase your speed.
You might clear now the speed is the rate of change of any quantity, here
we are talking about distance so; the rate of change of distance with respect
to time is called speed.
Important Formulae for Time and Distance
SPEED(v) = DISTANCE(d) / TIME(t)
(always remember this formula)
This is
the most important formula of this complete topic, we can derive some formula
by rearranging this formula.
DISTANCE(d) = SPEED(v) × TIME(t)
and
TIME(t) = DISTANCE(d) / SPEED(v)
E.g. A bike crosses a bridge with a speed of 108 km/h. What
will be the length of the bridge, if The bike takes 8 h to cross the bridge?
As we
know by our formula of distance
d = v ×
t
⇒ d = 108 × 8 =
864km (Ans.)
Very
easy one, let’s try to make this bit complicated.
E.g. A bike crosses a bridge with a speed of 40 m/s. What will
be the length of the bridge, if
the
bike takes 8 hours to cross the bridge?
TIP –
To
convert speed from km/h to m/s simply multiply in with “5 / 18” and when
converting m/s to km/h multiply the speed with “18 / 5”.
Easy to
remember? it saves plenty amount of time during the exam.
Let’s
get back to our question
⇒ v = 40 m/s or 40
× 18 / 5 = 144 km/h
Now
from the formula
d = v ×
t
⇒ d = 144 × 8 =
1152 km (Ans.)
Average Speed–
When a body travels with different speeds for different
durations, then the average speed of that body for the complete journey is
defined as the total distance covered by the body divided by the total time
taken to cover the distance.
Average speed = total distance / total time
Let’s
take an example to understand this concept really well.
E.g. A person covers a distance of 20 km by bus in 35 min.
After deboarding the bus, he took rest for 20 min and covers another 10 km by a
taxi in 20 min. Find his average speed for the whole journey.
Let’s
make this one very easy; we want to find out average speed, we require two
things total distance and total time taken.
Total
distance = 20 + 10 = 30 km
Total
time = 35 + 20 + 20 =75 min. or 75 /60 hours or 5 / 4 hours.
Average
speed = total distance / total time
⇒ 30 /(5 / 4) = 24
km/h (Ans.)
Important Formula:
When a
certain distance is covered at speed A and the
same distance is covered at speed B, then
the average speed during the whole journey is given by
⇒ 2AB / (A+B)
Let’s
take a simple example to learn this point very well.
E.g. Shantanu covers a certain distance by a car driving
at 35 km/h and he returns back to the starting point riding on a scooter with a
speed of 25 km/h. Find the average speed for the whole journey.
Let the
values of ‘A’ and ‘B’ be,
A = 35
km/h
B = 25
km/h
Average
speed = 2AB / (A+B)
⇒ 2 × 35 ×
25 / (25 + 35)
⇒ 1250 / 60
= 29.16 km/h (Ans.)
This
was really very important concept to know but questions wouldn’t be asked
directly, there would be the use of the concept of average speed so it’s
necessary for you to be comfortable with this.
E.g. A man is walking at a speed of 10 km/h. After every
kilometer he takes rest for 5 minutes, how much time would he take to cover a
distance of 5km.
Let’s
break time taken in two parts
Time
taken = time during rest + walking time
The
time during rest = no. of times he took rest × 5
For 5km
he would take rest for 4 times
Time
during rest = 4 × 5 = 20 min
Walking
time = 5 / 10 = 0.5 h or 30 min Total time = 30 + 20 = 50 min. (Ans.)
Continue
to Time and
Distance Part 2
Click here for Time and Distance
Video
All the
best
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