**SPEED, DISTANCE & TIME(TSD).**

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

Time and Distance Part 3

Time and Distance Part 4