Motion In A Plane

Question

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F₀e^–bt in the x direction. Its speed v(t) is depicted by which of the following curves?

Solution

straight F equals space straight F subscript 0 straight e to the power of negative bt end exponent rightwards double arrow space straight a space equals space straight F over straight m space equals space straight F subscript 0 over straight m straight e to the power of negative bt end exponent rightwards double arrow space dv over dt space equals straight F subscript 0 over straight m straight e to the power of negative bt end exponent integral dv space equals space integral subscript 0 superscript straight t straight F over straight m straight e to the power of negative bt end exponent dt rightwards double arrow space straight v space equals straight F over straight m open square brackets table row cell negative 1 end cell row straight b end table close square brackets open square brackets table row cell straight e to the power of negative bt end exponent end cell end table close square brackets subscript 0 superscript straight t rightwards double arrow space straight v equals space straight F over mb left square bracket straight e to the power of negative bt end exponent right square bracket straight v equals space 0 space at space straight t equals space 0 and space straight v rightwards arrow space straight F over mb space as space straight t rightwards arrow infinity

So, velocity increases continuously and attains a maximum value of v= F/mb as t ∞

Some More Questions From Motion in A Plane Chapter

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.

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Motion In A Plane

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F₀e^–bt in the x direction. Its speed v(t) is depicted by which of the following curves?

Some More Questions From Motion in A Plane Chapter

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?

Give two examples of polar vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F0e–bt in the x direction. Its speed v(t) is depicted by which of the following curves?

Some More Questions From Motion in A Plane Chapter

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?

Give two examples of polar vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F (t) = F₀e^–bt in the x direction. Its speed v(t) is depicted by which of the following curves?

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.