# Distance in time at acceleration

• dirty_d
In summary, the formula to find the time it takes for an object to travel a distance at a certain acceleration from a certain initial velocity is t = d / ((sqrt(pow(v0, 2) + 2 * a * d) + v0) / 2). This equation takes into account the initial velocity and can be used in scenarios such as a rocket accelerating towards the sun.
dirty_d
what is the formula to find the time it takes for an object to travel a distance at a certain acceleration from a certain initial velocity? I think I've figured out it without taking into account the initial v which would be t = squareroot( (d * 2) / a), i think... but I'm not sure how to fit the initial velocity in there.

Can you show some work?

dirty_d said:
what is the formula to find the time it takes for an object to travel a distance at a certain acceleration from a certain initial velocity? I think I've figured out it without taking into account the initial v which would be t = squareroot( (d * 2) / a), i think... but I'm not sure how to fit the initial velocity in there.

Start off with the equation $$d = d_{0}+v_{0}t+\frac{1}{2}at^2$$. The equation you got would be valid for d0 = v0 = 0.

Last edited:
radou i have no idea how to rearrange that formula, cyrusabdollahi, an example would be if a rocket is in space with the engine off traveling at 1000 m/s towards the sun and then turns the engine on and starts accelerating at 100 m/s/s in the same direction how long would it take to travel 1000 km towards the sun from when it starts accelerating.

What is your level of math?

level = low

anybody...

this works i don't know if it can be simplified any,

t = d / ((sqrt(pow(v0, 2) + 2 * a * d) + v0) / 2)

## What is distance in time at acceleration?

Distance in time at acceleration is a measure of the distance traveled by an object over a period of time while experiencing acceleration. Acceleration is defined as the rate of change of an object's velocity.

## How is distance in time at acceleration calculated?

Distance in time at acceleration is calculated using the formula d = 0.5at^2, where d is the distance, a is the acceleration, and t is the time.

## What is the relationship between distance, time, and acceleration?

The relationship between distance, time, and acceleration is defined by the equation d = vt + 0.5at^2, where d is the distance, v is the initial velocity, t is the time, and a is the acceleration. This equation shows that distance is directly proportional to time and acceleration.

## How does acceleration affect the distance traveled over time?

Acceleration affects the distance traveled over time by increasing the rate at which an object's velocity changes. This means that the object will cover a greater distance in a shorter amount of time when experiencing acceleration.

## What are some real-life examples of distance in time at acceleration?

Some real-life examples of distance in time at acceleration include a car accelerating from a stop, a ball falling due to gravity, and a rocket taking off into space. In all of these cases, the distance traveled by the object increases over time due to the acceleration it experiences.

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