Chat with us, powered by LiveChat

Position Vector, Velocity, and Acceleration

Instead of moving in a straight line, if a particle body moves in a curved path (traverses), motion of that particle body will be known as curvilinear motion.

Suppose a graph is constructed with x, y, z coordinates. At a certain time ‘t,’let the position vector of a particle ‘P’ be ‘r.’ After sometime, the position vector ‘P’ moves to another position, making the new position ‘P’’. Its new time interval stands to be ‘M’. Time associated with the new position (P’) is t + ∆t, and its new position vector is ‘r’’.

Position vector velocity and acceleration 1

After the graph is formed, you can see that in new time ‘M,’traversement of old point ‘P’ is to displacement ∆r.

Position vector velocity and acceleration 2

When the limit of the particle is ∆t à 0, and its average velocity is seen to be,

V =

Position vector velocity and acceleration 3

By combining the limit and velocity, you will get its instantaneous velocity, which is,

Position vector velocity and acceleration 4

From the above equation, scalar magnitude of ∆r is found to be,

As you already know that average speed of the particle body is, instantaneous speed of it stands to be at,

Position vector velocity and acceleration 5

Now, let velocities at both points be derived with a certain name. Let velocity of P be V and velocity of P’ be V.’ When particle body changes their positions and velocities, time regarding that displacement will also get changed. In this case, the new time will be ‘t + ∆t’ from t.

Position vector velocity and acceleration 6

So from this change, a new equation comes out,

On further calculation, you will see its average calculation to be,

Instantaneous acceleration of that particle in limiting case,

Position vector velocity and acceleration 7

The particle body P1 moves from P2 to P3, which cannot be stated as a path but a holograph. ‘A’ is found to be the tangent to that hodograph, which in this case is the acceleration of the motion. Also, changing ‘V’ is tangent to that particle path (hodograph). But when in consideration to the path of that particle, in ageneralized sense, ‘a’ cannot be termed as a tangent to that particle path.

Position vector velocity and acceleration 8

Finally, when you add all the tips of velocity, the newly formed curve is called hodograph, which is mentioned previously.

Position vector velocity and acceleration 9

 

Links of Previous Main Topic:-

Links of Next Mechanical Engineering Topics:-

 

Trustpilot

We’re rated Excellent

4.7 out of 5 based on 39 reviews

Join over 200,000+ happy students served our tutors

Take a look at independent reviews to see what users have to say about our homework help service.

4.5/5

overall rating
on LiveChat

96%

of users
recommend service

How It Works

1. Get Price Estimate.
1. Get Price Estimate.

Submit.

Send us your homework. Mention deadline & upload relevant files.

2. Pay Securely.
2. Pay Securely.

Pay.

We accept all major credit cards. Partial payments also accepted.

3. Get Solutions.
3. Get Solutions.

Delivered

Receive error-free, step-by-step solutions in your email.

FAQs

Why use Myhomeworkhelp?

We provide you with the homework help from top experienced experts. Your satisfaction is a priority to us. Get better grades or money-back. It’s that risk-free! Furthermore, everything about you is kept confidential.

How quickly can you help me with my homework?

We take pride in our 24×7 homework help services. Which means, student can approach us anytime, to get help even on short notices. As short as few hours! And yes, we provide complementary plagiarism-free report.

How much will it cost?

We do not have a monthly fees or minimum payments. Each homework task is quoted a unique price. It is based on tutor’s estimate of the time it will take them to complete your task. There are no obligations, and you are free to discuss the price quote with the tutor.
We do accept partial payment (subject to our policy) to start working on your assignment help. You can pay the remaining amount when your task gets completed. No pressure of up-front payment. No hidden costs.

Who are your tutors?

All our experts are highly qualified professionals – holding at least Master’s degree of their respective fields of expertise. We are very selective and choose only the best qualified tutors for each academic subject. All tutor applicants must provide academic transcripts for each degree they hold, and are tested and screened carefully by our staff.

I have privacy concerns. Can I trust you?

Myhomeworkhelp has completed over 250,000 homework help tasks over the last 12 years. But do not take our word for it! See our here and on Trustpilot. Furthermore, everything about you is kept confidential. Your credit card information is not stored anywhere, and use of PayPal relies on their secure payment networks. Your identity, payment and homework help are in safe hands.

Check our video

Our Reviews
Ratings