# Calculating Acceleration: Solving SUVAT and a Constant Homework Statement

• thejosh
In summary, the question presents a scenario where a vehicle accelerates from rest and travels a certain distance s1, then decelerates at a constant rate and travels a second distance s2 until it stops. The ratio s2/s1 is represented by the constant K, and the goal is to find the acceleration (a) of the vehicle in terms of K. However, the question itself is flawed as it allows for any value of a to satisfy the given conditions.
thejosh

## Homework Statement

A vehicle Accelerates from rest (a) and travels a certain distance s1 It then deccelerates (a) at a constant rate and travels a second distance s2 until it stops. If s2/s1 = K then what is the accleration (a) of the vehicle.

v=u+at
s=ut+1/2at^2
s=vt-1/2at^2
v^2=u^2 + 2as
s=(u+v)t/2

## The Attempt at a Solution

I used v^2=u^2 + 2as to describe the two parts of the journey but I ended up at a completely incorrect answer.

thejosh said:
A vehicle Accelerates from rest (a) and travels a certain distance s1 It then deccelerates (a) at a constant rate and travels a second distance s2 until it stops. If s2/s1 = K then what is the accleration (a) of the vehicle.

There is a problem her, You have a for both the accelaration and the deceleration, but if they are the same, you would need s1=s2, and the acceleration is can still be anything. Are you sure this is correct?

Sorry, you are actually supposed to make an expression for K using a as the link between the two parts of the journey.

thejosh said:
Sorry, you are actually supposed to make an expression for K using a as the link between the two parts of the journey.

There still seems to be missing something. Are the times of the acceleration and deceleration equal?

thejosh said:
A vehicle Accelerates from rest (a) and travels a certain distance s1 It then deccelerates (a) at a constant rate and travels a second distance s2 until it stops. If s2/s1 = K then what is the accleration (a) of the vehicle.
The question does not make sense as it stands. I suggest that there are two different magnitudes of acceleration, and you are supposed to find one of them in terms of K and the other acceleration.

You are supposed to find an expression by describing the two parts of the journey using suvat equations in terms of K the constant, the link IS a which is why they are the same, I tried using the suvat equation v^2=u^2+2as as there is no time in the equation it is just the linking and final conclusions that I struggled with.

You are supposed to find an expression by describing the two parts of the journey using suvat equations in terms of K the constant, the link IS a which is why they are the same, I tried using the suvat equation v^2=u^2+2as as there is no time in the equation it is just the linking and final conclusions that I struggled with.

thejosh said:
You are supposed to find an expression by describing the two parts of the journey using suvat equations in terms of K the constant, the link IS a which is why they are the same
As others have pointed out, the magnitudes of the acceleration and deceleration cannot be the same except for the trivial case where s1 = s2.

So did you mean to write "a" for both accelerations?

thejosh said:
You are supposed to find an expression by describing the two parts of the journey using suvat equations in terms of K the constant, the link IS a which is why they are the same, I tried using the suvat equation v^2=u^2+2as as there is no time in the equation it is just the linking and final conclusions that I struggled with.
Suppose, for example, that K=1. If it accelerates at a for distance s1=s it reaches speed v where v2=2as. If it now decelerates at a for s2=s it will come to a stop. Thus, we have met the conditions, yet a is anything at all.
Are you quite sure you have written out the question exactly as given to you, down to the last dot and comma?

thejosh
Thanks guys I solved it and as haruspex clearly pointed out I did not read the question carefully neither did I type it out correctly I am seriously sorry but I appreciate the help all the same, I just ran out of wifi for a while.

## 1. How do I calculate acceleration using the SUVAT equations?

The SUVAT equations are a set of five equations that relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). To calculate acceleration, you will need to know at least three of these variables, and then use the appropriate equation to solve for acceleration.

## 2. What is the difference between average and instantaneous acceleration?

Average acceleration refers to the overall change in velocity over a certain period of time, while instantaneous acceleration refers to the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the change in time, while instantaneous acceleration can be found by taking the derivative of the velocity function with respect to time.

## 3. How do I know which SUVAT equation to use?

The SUVAT equations are labeled as s = ut + 1/2at², v = u + at, v² = u² + 2as, s = (u+v)/2 x t, and s = ut + 1/2at². You will need to identify which variables are known and which one you are trying to find. Then, you can select the appropriate equation and rearrange it to solve for the unknown variable.

## 4. Can I use the SUVAT equations for non-uniform acceleration?

No, the SUVAT equations are only valid for constant acceleration. For non-uniform acceleration, you will need to use more advanced equations, such as the kinematic equations or the equations of motion.

## 5. What is the unit for acceleration?

The unit for acceleration is meters per second squared (m/s²). This means that for every second, the velocity changes by that amount. It can also be written as m·s⁻² or m s⁻².

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