The distance covered by accelerating body is
starting from rest ... d = 1/2 a t^2
with an initial velocity (v) ... d = 1/2 a t^2 + v t
what is the distance travelled
To calculate the distance covered by an accelerating body, you'll need the initial velocity (v0), the final velocity (v), and the acceleration (a). Assuming we're considering constant acceleration, you can use the following equation:
Distance = (v^2 - v0^2) / (2a)
1. Gather the values of the initial velocity (v0), final velocity (v), and acceleration (a).
2. Substitute the values into the formula: Distance = (v^2 - v0^2) / (2a).
3. Square the final velocity (v) and the initial velocity (v0).
4. Subtract the square of the initial velocity (v0^2) from the square of the final velocity (v^2).
5. Multiply the result by 1/ (2 times acceleration (a)).
6. Calculate the final result, which will be the distance covered by the accelerating body.
The distance covered by an accelerating body can be calculated using the basic equations of motion. There are three equations of motion that relate distance, time, initial velocity, final velocity, and acceleration:
1. 𝑑 = 𝑢𝑡 + (1/2)𝑎𝑡^2
2. 𝑣 = 𝑢 + 𝑎𝑡
3. 𝑣^2 = 𝑢^2 + 2𝑎𝑑
Where:
- 𝑑 is the distance covered
- 𝑢 is the initial velocity
- 𝑣 is the final velocity
- 𝑡 is the time taken
- 𝑎 is the acceleration
To calculate the distance covered, you need to know the initial velocity, final velocity, and acceleration, or alternatively, you can find these values if you have enough information. Here's a step-by-step guide on how to calculate the distance covered by an accelerating body:
1. Determine the given information: Identify the values you have from the problem or experiment. This could include the initial velocity (𝑢), final velocity (𝑣), time (𝑡), or acceleration (𝑎).
2. Determine which equation to use: Depending on the given information, determine which equation to use. If you have both initial and final velocities, acceleration, and time, Equation 3 can be used. If you have initial velocity, acceleration, and time, Equation 1 can be used. If you have initial velocity, acceleration, and final velocity, Equation 2 can be used.
3. Substitute the known values: Plug in the known values into the appropriate equation.
4. Solve for the unknown value: Rearrange the equation to solve for the unknown value, which is the distance covered (𝑑).
5. Calculate the distance: Substitute the values into the equation and calculate the distance covered by the accelerating body.
Remember to use consistent units throughout the calculations to obtain accurate results.