If speed doubles, by what factor is time reduced?

When speed doubles, the relationship between speed, time, and distance plays a crucial role in determining the change in time. To understand this relationship, we can reference the fundamental equation of motion which relates distance, speed, and time:

[ \text{Distance} = \text{Speed} \times \text{Time} ]

From this equation, we can derive time as:

[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} ]

If we maintain a constant distance and increase the speed, the time taken to cover that distance will be affected. Specifically, if the speed doubles, we can express the new time taken to cover the same distance with the new speed.

Let’s denote the initial speed as ( v ) and the initial time as ( t ). The time to cover a fixed distance ( d ) at the initial speed is:

[ t = \frac{d}{v} ]

If the speed increases to ( 2v ):

[ \text{New Time} = \frac{d}{2v} ]

Now, dividing ( d ) by ( 2v ) shows that the new time is half of the original time:

[ \