Time and Distance – Formulas

 Time and Distance – Formulas

Distance is the numerical measure of how far a point or an object is from another point or object. Time is the measure of the time taken for an entity to reach from one point to another. Lastly, the measure of how fast or slow an object or a point moves is known as speed.

Speed, distance and time are related to each other by the formula:

 

1.Speed = DistanceTime$\frac{\text{Distance}}{\text{Time}}$

 

So, speed can be defined as the distance traveled per unit time. It indicates the rate at which an object moves between two points.
The formula connecting speed, distance and time can also be given as:

 

x=dt$x=\frac{d}{t}$

 

Where,

x$x$ = Speed

d$d$ = Distance traveled

t$t$ = Time taken

 

Distance is measured in units of length like meters, kilometers, miles and other units like feet or inches. Time is measured in seconds, minutes and hours. Speed is measured in distance per unit time, for example, meters per second (m/s), kilometers per hour (km/hour), or miles per hour.

 

The above formula can also be used to determine distance or time.

 

• 2.Distance = Speed  X Time (or) d= x X t
  
  
  
• 3.Time = Distance/Speed DistanceSpeed=dx$\frac{\text{<br>}}{}$

Therefore, distance is the product of speed and time, and time is distance per unit speed.

4.km/hr to m/sec conversion: formula -

Step-1 : Given Data

The given unit is km/hr.

We are required to convert it to m/s.

Step-2 : Explanation

SI unit of distance is a meter and of time is second according to the international system of units.

1km = 1000m

1hr = 60min

1min = 60sec

Therefore 1 hr = 60X60 sec = 3600 sec

Step 3: Calculation 

SO 1 km/hr = 1000/36000 m/s

      =5/8 m/s

      =0.28 m/s

so, to convert km/h to m/s we multiply the given number by 5/8 m/s or 0.28 m/s

5. m/sec to km/hr conversion : formula -(V m/sec =V x18/5)

1.meters per second(m/s) and kilometers per hour (km/h) are units of speed(scalar) velocity(vector).

2.kilometers per hour(km/h) measures the distance covered in number of kilometers per one hour and meters per second (m/s) measures the distance covered in number of meters per one second.

3.to convert meters into kilometers, the quantity is divided by 1000 and to convert seconds into hours, the quantity is divided by 3600.

4.So, to convert m/s to km/h, the numerator must be divided by 1000 and the denominator must be divided by 3600. This implies that the whole quantity that is given in m/s must be divided by 3600. This implies that the whole quantity that is given in m/s must be multiplied by 3600/1000.

5.Converting it in least form, the quantity given in m/s must be multiplied by 18/5 to convert it into km/h.

If the ratio of the speeds of A and B is a:b , then the ratio of the times taken by them to cover the same distance is 1/a : 1/b or b:a.

Suppose a man covers a certain distance at X km/hr and an equal distance at Y km/hr. Then,

the average speed during the whole journey is 2xy/x+y km/hr.

Solved Examples

Example 1: Laura was going to the mall from her house in her car at an average speed of 36 mph. She took 0.2 hours to reach the mall. Calculate the distance she traveled from her house to the mall?

 

Solution:
Speed of the car, x$x$ = 36 mph

 

Time taken by the car to reach the mall, t$t$ = 0.2 hr

 

We need to find the distance covered by Laura.

 

The formula relating speed, distance and time is,

 

Distance traveled, d=x×t$\mathrm{d }= \mathrm{x }\times t$

 

d=36×0.2$d= 36\times 0.2$  Substitute 36 for x$x$ and 0.2 for t$t$

 

   =7.2$=7.2$           Multiply

 

Therefore the distance traveled by Laura from her house to the mall is 7.2 miles.

 

Example 2:

Ronald covered a distance of 280 miles in 4 hours on his motorbike. Calculate how fast the bike would have moved to cover this distance.

 

Solution:

Distance covered, d$d$ = 280 miles,

 

Time taken, t$t$ = 4 hours

 

x=dt$x=\frac{\mathrm{d/}}{t}$     Formula for speed

 

x=2804$x=\frac{\mathrm{280/}}{4}$  Substitute 280 for d and 4 for t$t$

 

x=70$x=70$ Divide

 

Therefore, the bike would have moved at a speed of 70 miles per hour to cover a distance of 280 miles.

 

Example 3: In a cycle race, cyclist A is moving with a speed of 2 km/hr and cyclist B is moving at a speed of 3 km/hr. The cyclists need to cover a distance of 12 km to reach the destination. Which cyclist will reach the destination first?

 

Solution:

To determine which cyclist reaches the destination, first, we need to compare the time taken by each cyclist to reach the destination.

 

Speed of cyclist A, xa$x_a$ = 2 km/hr

 

Speed of cyclist B, xb$x_b$ = 3 km/hr

 

Distance covered by both the cyclists, d$d$ = 12 km

 

We need to find the time taken by cyclist A and cyclist B.

 

t=dx$t=\frac{\mathrm{d/}}{x}$              Formula for time taken

 

ta=122=6$t_a=\frac{\mathrm{12/}}{2}=6$    Substitute 12 for d$d$ and 2 for x$x$ and solve

 

tb=123=4$t_b=\frac{\mathrm{12/}}{3}=4$    Substitute 12 for d$d$ and 3 for x$x$ and solve

 

So the time taken by cyclist A is 6 hours and the time taken by cyclist B is 4 hours.

Now since 6 hours is greater than 4 hours, that is, cyclist B takes less time to reach the destination.

Therefore cyclist B will reach the destination first.

$\frac{5}{1}$$0.28m$