Solve Mechanics Problem: Find Magnitude of Force at t=2s

[HMPARTICLE]

1. The problem

A 3 kg object is moving in a plane with its x and y coordinates given by x = 5t^2 -1 and y = 3t^3 +2 where x and y are in meters and t is in seconds. Find the magnitude of the new force acting on this object at t= 2s

2. My attempt.

So my first attempt is to find a vector expression for acceleration. I integrated the expressions for x and y to give

V subx = 5/3 t^3 -t +c

To find the constant on integration I found the position of the particle at t=0 and t=2. Therefore calculating the velocity at 2 seconds. Thus the constant of integration for this expression is -4/3

The velocity at 2s being 10i+12j ms^-1

I have done the exact same process for velocity in the y direction and reached an expression for Vsuby .

My problem is I'm not sure how to get a valid expression for acceleration, and this seems like a really long winded way of answering this question.

 

[Quesadilla]

If you have an expression $\mathbf{r}(t) = (x(t), y(t))$ for position, wouldn't velocity be $\dot{ \mathbf{r}}$ and acceleration $\ddot {\mathbf{r}}$?

 

[Ray Vickson]

1. The problem

A 3 kg object is moving in a plane with its x and y coordinates given by x = 5t^2 -1 and y = 3t^3 +2 where x and y are in meters and t is in seconds. Find the magnitude of the new force acting on this object at t= 2s

2. My attempt.

So my first attempt is to find a vector expression for acceleration. I integrated the expressions for x and y to give

V subx = 5/3 t^3 -t +c

To find the constant on integration I found the position of the particle at t=0 and t=2. Therefore calculating the velocity at 2 seconds. Thus the constant of integration for this expression is -4/3

The velocity at 2s being 10i+12j ms^-1

I have done the exact same process for velocity in the y direction and reached an expression for Vsuby .

My problem is I'm not sure how to get a valid expression for acceleration, and this seems like a really long winded way of answering this question.

Why are you integrating? How are force and acceleration related? Define acceleration!

 

[HMPARTICLE]

The net force on the object is the product of mass and acceleration. However I am being asked for the magnitude of the force on the object. I'm struggling to see how I can work with the expression for its displacement to get an expression for its acceleration so I can multiply its mass to get an expression for the net force

 

[Orodruin]

How is the position related to velocity? How is velocity related to acceleration?

 

[HMPARTICLE]

Got it! God I'm such a simpleton at times! I was inter grating when I should have been differentiating :(