# 1-D (I think) Speed to distance problem

• magnanimousto
In summary, the problem involves a runner exerting a constant force to accelerate from rest to 2.0 m/s over a distance of 12 m and the question asks for the total distance needed to accelerate from rest to 3.0 m/s. The answer is 27 m and the solution involves using the basic kinematic equations or the Work-Energy Theorem to find the acceleration and then using that value to solve for the total distance.
magnanimousto

## Homework Statement

A runner exerts a constant force to accelerate from rest to 2.0 m/s over a distance of 12 m.
Assuming the runner can keep up the same force, what total distance would be needed to ac-
celerate up from rest to 3.0 m/s?

none given.

## The Attempt at a Solution

The answer to the problem is 27. After quite some time spent thinking I tried solving first part for time using x= 1/2 vt and then plugging it into 2nd part. but that gives time as 12 and 2nd x as 18 so wrong. Dunno how to solve it

magnanimousto said:

## Homework Statement

A runner exerts a constant force to accelerate from rest to 2.0 m/s over a distance of 12 m.
Assuming the runner can keep up the same force, what total distance would be needed to ac-
celerate up from rest to 3.0 m/s?

none given.

## The Attempt at a Solution

The answer to the problem is 27. After quite some time spent thinking I tried solving first part for time using x= 1/2 vt and then plugging it into 2nd part. but that gives time as 12 and 2nd x as 18 so wrong. Dunno how to solve it
Hello magnanimousto. Welcome to PF!

What kinematic equations do you know?

Alternatively, do you know the Work-Energy Theorem ?

This is a constant acceleration problem, so you can use the basic kinematic equations for that case. Try solving for the acceleration first, and using that value for the next part.

If you don't know those equations, here's the one you should probably use -- they're very helpful to memorize though.
$v_{f}^{2}= v_{i}^{2} + 2aΔd$

Thanks jackarms & SammyS.I do know kinematics equations, for some reason it never occurred to me that since the force is the same in both so must be the acceleration

.

I would approach this problem by using the equations of motion, specifically the equation v^2 = u^2 + 2as. In this problem, u (initial velocity) is 0 m/s, v (final velocity) is 2.0 m/s, and a (acceleration) is unknown. We can rearrange the equation to solve for a: a = (v^2 - u^2)/2s. Plugging in the values, we get a = (2.0^2 - 0)/2(12) = 0.1667 m/s^2.

Now, we can use this acceleration value to solve for the total distance needed to accelerate to 3.0 m/s. Again, using the same equation, we have v^2 = u^2 + 2as, but this time v is 3.0 m/s and u is still 0 m/s. Plugging in a = 0.1667 m/s^2, we get s = (3.0^2 - 0)/2(0.1667) = 27 m. This is the total distance needed to accelerate from rest to 3.0 m/s.

In summary, the key to solving this problem is to use the equations of motion and to carefully consider the given information. By finding the acceleration in the first part of the problem, we can use it to solve for the total distance in the second part. It is important to carefully label and organize the given values in order to apply the equations correctly.

## 1. What is the formula for calculating speed in a 1-D problem?

In a 1-D speed to distance problem, the formula for calculating speed is speed = distance/time. This means that the speed is equal to the distance traveled divided by the time it took to travel that distance.

## 2. How do I convert between different units of speed in a 1-D problem?

To convert between different units of speed in a 1-D problem, you can use a conversion factor. For example, to convert from miles per hour (mph) to meters per second (m/s), you can multiply the speed in mph by 0.44704.

## 3. What is the difference between average speed and instantaneous speed in a 1-D problem?

Average speed is the total distance traveled divided by the total time taken, while instantaneous speed is the speed at a specific moment in time. In a 1-D problem, average speed is usually used to calculate the overall speed, while instantaneous speed can be used to determine the speed at a certain point in the journey.

## 4. How do I calculate the distance traveled in a 1-D problem if I know the speed and time?

To calculate the distance traveled in a 1-D problem, you can use the formula distance = speed x time. This means that the distance traveled is equal to the speed multiplied by the time taken to travel that distance.

## 5. Can I use the same formula for calculating speed in a 1-D problem for all types of motion?

Yes, the formula speed = distance/time can be used for all types of motion in a 1-D problem. However, the units of distance and time may vary depending on the type of motion (e.g. linear, circular, or accelerated) and the units of speed may need to be converted accordingly.

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