Chapter 4: Q13P (page 84)

A particle moves so that its position (in meters) as a function of time (in seconds) is $\overset{⇀}{r} = \hat{i} + 4 t^{2} \hat{j} + t \hat{k}$ . Write expressions for: (a) its velocity and (b) its acceleration as functions of time.

Short Answer

Expert verified

(a) The velocity is $((8 t) \hat{j} + \hat{k)} m / s$

(b) The acceleration is $8 \hat{j} m / s^{2}$

Step by step solution

Given information

It is given that,

$\overset{⇀}{r} = \hat{i} + 4 t^{2} \hat{j} + t \hat{k}$

To understand the concept

This problem deals with simple algebraic operation that involves calculation of velocity and the acceleration at given time. Velocity is the rate of change of its position and the acceleration is the rate of change of velocity with respect to time. Thus the velocity vector and acceleration can be expressed using the standard equation for the velocity and acceleration.

Formulae:

$\overset{⇀}{v} = \frac{d \overset{⇀}{r}}{dt} (i) Where, \overset{⇀}{r} is the position vector \overset{⇀}{a} = \frac{d \overset{⇀}{v}}{dt} (i i)$

(a) To find the velocity

Velocity can be expressed by substituting the value of $\overset{⇀}{r}$ in equation (i)

$\overset{⇀}{v} = \frac{d (\hat{i} + 4 t^{2} \hat{j} + t \hat{k})}{dt}$

Thus,

$\overset{⇀}{v} = ((8 t) \hat{j} + \hat{k}) m / s$

(b) To find the acceleration

Acceleration can be expressed by substituting the value of $\overset{⇀}{v}$ in equation (ii)

$\overset{⇀}{a} = \frac{d ((8 t) \hat{i} + \hat{k})}{dt}$

Thus, the acceleration is

$\overset{⇀}{a} = 8 \hat{j} m / s^{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A particle moves so that its position (in meters) as a function of time (in seconds) is $\overset{⇀}{r} = \hat{i} + 4 t^{2} \hat{j} + t \hat{k}$ . Write expressions for: (a) its velocity and (b) its acceleration as functions of time.

Short Answer

Step by step solution

Given information

To understand the concept

(a) To find the velocity

(b) To find the acceleration

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Magnetism

Solid State Physics

Classical Mechanics

Dynamics

Electromagnetism

Study anywhere. Anytime. Across all devices.

A particle moves so that its position (in meters) as a function of time (in seconds) is r⇀=i^+4t2j^+tk^. Write expressions for: (a) its velocity and (b) its acceleration as functions of time.

Short Answer

Step by step solution

Given information

To understand the concept

(a) To find the velocity

(b) To find the acceleration

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Magnetism

Solid State Physics

Classical Mechanics

Dynamics

Electromagnetism

Study anywhere. Anytime. Across all devices.

A particle moves so that its position (in meters) as a function of time (in seconds) is $\overset{⇀}{r} = \hat{i} + 4 t^{2} \hat{j} + t \hat{k}$ . Write expressions for: (a) its velocity and (b) its acceleration as functions of time.