Speed Distance and Time

Concepts

Essential Blocks Advance Subtitle

Speed and Distance Formulas Explained

Speed:

$\text{Speed} = \frac{\text{distance}}{\text{time}}$

The formula for speed indicates how fast an object is moving. It is calculated by dividing the distance traveled by the time taken to cover that distance. This basic formula is fundamental in understanding motion.
Time to Meet:

$\text{Time to meet} = \frac{\text{distance}}{\text{sum of speeds}}$

This formula is used when two objects are moving towards each other. The time to meet is determined by dividing the distance between them by the sum of their speeds. This is applicable in scenarios where two vehicles or entities are approaching each other, and we want to find out when they will intersect.
Creating Gap Distance ‘d’:

$d = \frac{\text{distance}}{\text{sum of speeds}}$

The gap distance ‘d’ refers to the distance created between two objects when they start moving apart or closing in. This is calculated similarly to the time to meet but expresses the physical distance covered rather than the time.
Overtaking Time:

$\text{Overtaking time} = \frac{\text{gap distance} \times s_1}{\text{difference of speeds}}$

This formula is used to calculate the time it takes for one object to overtake another. Here, $s_1$ is the speed of the faster object, and the difference of speeds is the relative speed between the two. The gap distance represents the initial distance between the two objects before overtaking starts.
Average Speed of the Whole Trip:

$\text{Average Speed} = \frac{2s_1s_2}{s_1 + s_2}$

This formula calculates the average speed when an object travels two segments of a journey at different speeds, $s_1$ and $s_2$ . It is particularly useful when the time or distance for each segment is the same. The formula takes into account the harmonic mean of the speeds to determine the overall average speed.