# Particle Motion Problems: motion is given by x=-2t2 and y=t3-3t+9, t>0

#### 7equestrian7

##### New member
Hi, I'm in AP Calculus BC, but I'm on medical leave without a teacher or tutor, so I'm stuck on a couple problems. Please show me how to do these, it would be greatly appreciated!

1. The motion of a particle is given by x=-2t2 and y=t3-3t+9, t>0. Find the coordinates of the particle when its instantaneous direction of motion is horizontal.

I know the answer is (-2, 7) but I'm not quite sure how to get there. I have started by finding dx/dt= -4t and dx/dy= 3t2-3, but unsure of where to go from here.

2. The motion of a particle is given by x=lntand y=t2-4t. Find the coordinates of the particle when its instantaneous direction of motion is horizontal.

I know the answer is (ln2, -4) but I'm not quite sure how to get there. I have started by finding dx/dt= 1/t and dy/dt= 2t-4, but unsure of where to go from here.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi, I'm in AP Calculus BC, but I'm on medical leave without a teacher or tutor, so I'm stuck on a couple problems. Please show me how to do these, it would be greatly appreciated!

1. The motion of a particle is given by x=-2t2 and y=t3-3t+9, t>0. Find the coordinates of the particle when its instantaneous direction of motion is horizontal.

I know the answer is (-2, 7) but I'm not quite sure how to get there. I have started by finding dx/dt= -4t and dx/dy= 3t2-3, but unsure of where to go from here.

2. The motion of a particle is given by x=lntand y=t2-4t. Find the coordinates of the particle when its instantaneous direction of motion is horizontal.

I know the answer is (ln2, -4) but I'm not quite sure how to get there. I have started by finding dx/dt= 1/t and dy/dt= 2t-4, but unsure of where to go from here.
That is not correct - how did you get that?

Instantaneous velocity is always in tangential direction. Which direction is horizontal?

What does it say about the tangential direction at the moment in question?

#### 7equestrian7

##### New member
That is not correct - how did you get that?

Instantaneous velocity is always in tangential direction. Which direction is horizontal?

What does it say about the tangential direction at the moment in question?
Thanks for responding.
Sorry, it would be dy/dt. And horizontal would be the x direction. I'm still not sure what to do though.

#### Subhotosh Khan

##### Super Moderator
Staff member
Thanks for responding.
Sorry, it would be dy/dt. And horizontal would be the x direction. I'm still not sure what to do though.
If the tangent to the curve is parallel to x-axis - what can you say about dy/dx of the curve at that point?

#### 7equestrian7

##### New member
If the tangent to the curve is parallel to x-axis - what can you say about dy/dx of the curve at that point?
dy/dx would be equal to zero, because the slope would be zero when the curve is parallel to the x-axis, correct? But that would be at the points -1 and 1, which aren't the answers.

#### Dr.Peterson

##### Elite Member
dy/dx would be equal to zero, because the slope would be zero when the curve is parallel to the x-axis, correct? But that would be at the points -1 and 1, which aren't the answers.
But it's not x or y that is equal to 1 or -1! What is it that you solved for? What are the conditions on that variable? And what point does it give you?

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#### 7equestrian7

##### New member
But it's not x or y that is equal to 1 or -1! What is it that you solved for? What are the conditions on that variable? And what point does it give you?
I understand!I plug 1 into the original equations to get the x and y values. I got both of them.Thanks so much for the help, sorry I'm so slow to understand.

#### mmm4444bot

##### Super Moderator
Staff member
… sorry I'm so slow to understand.
Nobody need apologize for the rate at which they learn something! (Only a one-size-fits-all approach assumes that math students ought to progress at an equal, general rate. The notion that individual humans gain comprehension at a fixed rate is one of several disproven myths about how humans learn.)

Choose a group of people whom you respect (eg: professional athletes, distinguished medical experts, translators fluent in a dozen languages, famous artists). Did they all achieve success at the same rate?

What's important is that you're learning! You've grown the connections in your brain, and you now know more than you did last month. Keep up the good work, and you will reach your goals!