# Time and Distance

## What are Speed, Time and Distance?

Speed, time and distance are the three major concepts in physics. Speed is the rate of motion of an object between two points over a particular period of time which is measured in metres per second (m/s). Time is calculated by reading a clock, and it is a scalar quantity that do not change with direction. Distance is the total amount of ground covered by an object.

Speed of a body is the distance covered by the body per unit time i.e. Speed = Distance/Time.

Speed: Speed is the rate at which a particular distance is covered by an object in motion.

Time: Time is an interval separating two events.

Distance: Distance is the extent of space between two points.

### Units of Speed Time and Distance

Each of the speed, distance and time can be represented in different units:

• Time can be generally expressed in terms of seconds(s), minutes (min) and hours (hr).
• Whereas the distance is generally expressed in meters (m), kilometres (km), centimetres, miles, feet, etc.
• Speed is commonly expressed in m/s, km/hr.

### Relationship Between Speed, Time & Distance

• Speed = Distance/Time – This tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.
• Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,
• Distance = Speed X Time, and
• Time = Distance / Speed, as the speed increases the time taken will decrease and vice versa.

### Speed, Time & Distance Conversions

• To convert from km / hour to m / sec, we multiply by 5 / 18. So, 1 km / hour = 5 / 18 m / sec
• To convert from m / sec to km / hour, we multiply by 18 / 5. So, 1 m / sec = 18 / 5 km / hour = 3.6 km / hour
• Similarly, 1 km/hr = 5/8 miles/hour
• 1 yard = 3 feet
• 1 kilometer= 1000 meters = 0.6214 mile
• 1 mile= 1.609 kilometer
• 1 hour= 60 minutes= 60*60 seconds= 3600 seconds
• 1 mile = 1760 yards
• 1 yard = 3 feet
• 1 mile = 5280 feet
• 1 mph = (1 x 1760) / (1 x 3600) = 22/45 yards/sec
• 1 mph = (1 x 5280) / (1 x 3600) = 22/15 ft/sec
• For a certain distance, if the ratio of speeds is a : b, then the ratio of times taken to cover the distance would be b : a and vice versa.

## Application of Speed, Time & Distance

### 1. Average Speed

The formula for speed, time and distance is a calculation of the total distance an object travels over a given amount of time. It is a scalar quantity, meaning it’s an absolute value with no direction. To calculate it, you need to divide the total distance traveled by the amount of time it took to cover that distance.

Average Speed = (Total distance traveled)/(Total time taken)

Case 1 – When the distance is constant: Average speed = 2xy/x+y; Where, x and y are the two speeds at which the same distance has been covered.

Case 2 – When the time taken is constant: Average speed = (x + y)/2; Where, x and y are the two speeds at which we traveled for the same time.

2. Relative speed: The rate at which two moving bodies are separating from or coming closer to each other.

Case 1: If two objects are moving in opposite directions, then their relative speed would be S1 + S2

Case 2: If they were moving in the same direction, their relative speed would be S1 – S2

### 3. Inverse Proportionality of Speed & Time

Speed is inversely proportional to Time when the Distance is constant. S is inversely proportional to 1/T when D is constant. If the Speeds are in the ratio m:n then the Time taken will be in the ratio n:m.

This relation can be mathematically expressed as S = D/T where S (Speed), D (Distance) and T (Time).

To solve problems based on this relationship, two methods are used:

1. Inverse Proportionality Rule
2. Constant Product Rule.

### 4. Meeting Point Questions

If two people travel from two points A and B towards each other, and they meet at point P. The total Distance covered by them on the meeting will be AB. The Time taken by both of them to meet will be the same. As the Time is constant, Distances AP and BP will be in the ratio of their Speed. Say that the Distance between A and B is d.

If two people are walking towards each other from A and B, When they meet for the first Time, they together cover a Distance “d” When they meet for the second Time, they together cover a Distance “3d” When they meet for the third Time, they together cover a Distance of “5d”……