Work and Force in Physics

The video tutorial explains how to calculate the work done by an electric force on a charged particle moving along a straight line. It begins with the problem statement and introduces the concept of electric force. The path of the particle is parametrized, and the magnitude of the position vector and its derivative are calculated. The force function is set up, and the integral is evaluated using u-substitution to find the work done. The tutorial concludes with the final calculation and result.

What is the formula for the force exerted by an electric charge at the origin on a charged particle?

• F(r) = k * r / |r|^3

• F(r) = k / r^2

• F(r) = k * |r|^3

• F(r) = k * r^2

What is the constant 'k' assumed to be in the given problem?

• 15

• 20

• 10

• 5

How is the work done by a particle moving along a straight line calculated?

• By finding the area under the curve

• By calculating the line integral along the curve

• By multiplying force and distance

• By using the Pythagorean theorem

What is the y-component of the position vector r(t) in the parametrization?

• 2t

• 3t

• t^2

• t

What is the magnitude of the position vector r(t) simplified to?

• sqrt(4 + 13t^2)

• sqrt(4t^2 + 9t^2)

• sqrt(2^2 + 2t^2 + 3t^2)

• sqrt(13t^2)

What is the z-component of the derivative r'(t)?

• t

• 3

• 2

• 0

What is the x-component of the force function F(r(t))?

• 20 / (4 + 13t^2)^(3/2)

• 10 / (4 + 13t^2)^(3/2)

• 30t / (4 + 13t^2)^(3/2)

• 40t / (4 + 13t^2)^(3/2)

What substitution is used to evaluate the integral for work done?

• u = 2t^2 + 3t^2

• u = 4 + 13t^2

• u = 13t^2

• u = 4t^2 + 9t^2

What is the exact value of the work done as the particle moves along the straight line?

• -5 / sqrt(17) + 10

• 5 / sqrt(17) + 10

• 10 / sqrt(17) - 5

• -10 / sqrt(17) + 5

What is the approximate decimal value of the work done?

• 2.7182

• 1.6180

• 3.1415

• 2.5746