Question

What is the formula for distance, time and acceleration to get to speed

Answer 1

The formula relating distance, time, and acceleration to speed is rooted in the kinematic equations of motion. The most relevant equation for constant acceleration from rest is v = √(2 × a × d), which calculates the final velocity based on distance and acceleration.

Step-by-step explanation:

The formula a student is seeking connects distance, time, and acceleration to determine final speed. To find the relationship between these variables, consider the following equation which is derived from the kinematic equations for uniform acceleration:

v = √(2 × a × d)

This assumes that the initial speed (v0) is zero. Here's how to work through the problem:

1. Identify the given values for distance (d) and acceleration (a).
2. Insert these values into the equation.
3. Calculate the value under the square root first, which is twice the acceleration times the distance.
4. Take the square root of the result to find the final velocity (v).

It's important to remember that these equations apply to situations with constant acceleration. Also, this specific equation does not take initial speed into account and assumes it starts from rest. For complete understanding, explore the subject further in kinematics and motion modules where average speed, acceleration, and other concepts are covered in more detail.

Answer 2

The equations of motion are:

`v=u+at\\v^2=u^2+2as\\s=ut+(1)/(2)at^2`

Hence, the formula for distance (or displacement (s) ), time (t), and acceleration (a) to get to speed (u), is:

`s = ut+(1)/(2) at^2`