A body of mass m accelerates uniformly from rest to v₁ in time t₁. The instantaneous power delivered to the body as a function of time t is

$fraction numerator mv subscript 1 straight t over denominator straight t subscript 1 end fraction$
$fraction numerator mv subscript 1 superscript 2 space straight t over denominator straight t subscript 1 superscript 2 end fraction$
$fraction numerator mv subscript 1 straight t squared over denominator straight t subscript 1 end fraction$
$fraction numerator mv subscript 1 superscript 2 straight t over denominator straight t subscript 1 end fraction$

Solution

fraction numerator mv subscript 1 superscript 2 space straight t over denominator straight t subscript 1 superscript 2 end fraction

Let the constant acceleration of body of mass m is a.
From equation of motion
v₁ = 0 + at₁
⇒ a = t₂/t₁= ...... (i)
At an instant t, the velocity v of the body v = 0 + at
$straight v space equals space straight v subscript 1 over straight t subscript 1 straight t space space.... space left parenthesis ii right parenthesis therefore space instantaneous space power straight p space equals Fv space equals mav space space left parenthesis because space straight F space equals space ma right parenthesis equals space straight m open parentheses straight v subscript 1 over straight t subscript 1 close parentheses space straight x open parentheses straight v subscript 1 over straight t subscript 1 space straight x space straight t close parentheses space left square bracket space From space equ space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space equals space fraction numerator mv subscript 1 superscript 2 straight t over denominator straight t subscript 1 superscript 2 end fraction$

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A body of mass m accelerates uniformly from rest to v1 in time t1. The instantaneous power delivered to the body as a function of time t is

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.