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

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

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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

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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

Mechanics and Materials

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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.