Formula for Speed, Distance and Time
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:
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
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:
\(x=\frac{d}{t}\)
Where,
\(x\) = Speed
\(d\) = Distance traveled
\(t\) = 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.
- Distance = Speed \(\times\) Time (or) \(d\ =\ x\ \times\ t\)
- Time = \(\frac{\text{Distance}}{\text{Speed}} = \frac{d}{x}\)
Therefore, distance is the product of speed and time, and time is distance per unit speed.
Rapid Recall
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, \(x\) = 36 mph
Time taken by the car to reach the mall, \(t\) = 0.2 hr
We need to find the distance covered by Laura.
The formula relating speed, distance and time is,
Distance traveled, \(d=x \times t\)
\(d=36 \times 0.2\) Substitute 36 for \(x\) and 0.2 for \(t\)
\(=7.2\) 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, \(d\) = 280 miles,
Time taken, \(t\) = 4 hours
\(x=\frac{d}{t}\) Formula for speed
\(x =\frac{280}{4}\) Substitute 280 for d and 4 for \(t\)
\(x=70\) 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, \(x_a\) = 2 km/hr
Speed of cyclist B, \(x_b\) = 3 km/hr
Distance covered by both the cyclists, \(d\) = 12 km
We need to find the time taken by cyclist A and cyclist B.
\(t=\frac{d}{x}\) Formula for time taken
\(t_a = \frac{12}{2}=6\) Substitute 12 for \(d\) and 2 for \(x\) and solve
\(t_b = \frac{12}{3}=4\) Substitute 12 for \(d\) and 3 for \(x\) 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.
The rate of change of the position of an object in any direction is called the speed of the object.
The ratio of distance traveled or covered by an object to its unit speed is defined as time.
Distance is the numerical measure of how far a point or an object is from another point or object. Distance is calculated as the product of speed and time.
For a given speed, if the distance is doubled then the time taken will also be doubled.