# What Is the Rate of Change of Acceleration at t=2?

• LT72884
In summary, you need to figure out the rate of change of acceleration to find the instantaneous acceleration.
LT72884
Homework Statement
A particle traveled in a straight line in such a way that its distance (S) from a given point on that line after time (t) was S= 20t^3 -t^4 The rate of change of acceleration at time t=2 is what value?
Relevant Equations
S = 20t^3 - t^4
A particle traveled in a straight line in such a way that its distance (S) from a given point on that line after time (t) was S= 20t^3 -t^4 The rate of change of acceleration at time t=2 is what value?ok, I am kind of stuck on this very simple problem. It should be as simple as taking the derivative twice, and plugging in 2 at the end..
so if S = 20t^3 - t^4 then
V = 60t^2 - 4t^3 and
acceleration = 120t-12t^2 plug in 2 for t and it should be 240-48 = 192 but apparently the answer is 72... why?

am i not finding acceleration but really finding jerk? so i needed to do 3 derivs?
thanks

sysprog
LT72884 said:
am i not finding acceleration but really finding jerk? so i needed to do 3 derivs?
Yep.

BvU, sysprog and LT72884
Is it because it says find the rate of change of acceleration? If so, its one of them trick questions hahahaha

Defo: rate of change of acceleration ##\equiv \dot{a} = \ddot{v} = \dddot{s}##

PeroK, sysprog and LT72884
Well, SOB, they done tricked me with their fancy words haha

thanks

ergospherical
LT72884 said:
Is it because it says find the rate of change of acceleration? If so, its one of them trick questions hahahaha
It's not a trick, it's what rate of change means.
Given an expression for displacement as a function of time:
Instantaneous velocity = rate of change of displacement = 1st derivative of displacement
Instantaneous acceleration = rate of change of velocity = 2nd derivative of displacement
Instantaneous jerk = rate of change of acceleration = 3rd derivative of displacement
:
As far as you like.
You are asked for the rate of change of acceleration, not the instantaneous acceleration.

sysprog
Just chiming in on what @ergospherical and @haruspex have already said nicely: {assuming single vector here) first derivative of position wrt time is velocity; second is acceleration, third is jerk (rate of increase or decrease in acceleration), fourth is jounce (or snap, in case, no really, some guys enjoy this, you want to call the fifth and sixth crackle and pop -- as if anyone who doesn't listen to the musical explosions of his wilting rice krispies should care ) ##-## so yes, you really do have to figure the third derivative, and don't you of course step-by-step need the first and second to get to the third?

LT72884 said:
but apparently the answer is 72...
##72 km/h##, ##72 m/s## or ##72## something else?

## 1. What is the rate of change of acceleration?

The rate of change of acceleration is a measure of how quickly the acceleration of an object is changing over time. It is calculated by dividing the change in acceleration by the change in time.

## 2. How is the rate of change of acceleration related to velocity?

The rate of change of acceleration is directly related to velocity. When acceleration is constant, the rate of change of acceleration is equal to the acceleration itself. However, when acceleration is changing, the rate of change of acceleration will affect the change in velocity over time.

## 3. What factors can affect the rate of change of acceleration?

The rate of change of acceleration can be affected by various factors such as the mass of the object, the force applied to the object, and the surface or medium the object is moving through. Other factors such as air resistance and friction can also play a role in the rate of change of acceleration.

## 4. How is the rate of change of acceleration measured?

The rate of change of acceleration is typically measured in meters per second squared (m/s²) or feet per second squared (ft/s²). This is because acceleration is a change in velocity over time, and velocity is measured in units of distance per time.

## 5. Why is the rate of change of acceleration important in physics?

The rate of change of acceleration is important in physics because it helps us understand how objects move and how forces affect their motion. It is a fundamental concept in Newton's laws of motion and is used in various calculations involving motion, such as calculating the force needed to accelerate an object to a certain velocity.

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