Dynamics: Kinematics and Kinetics

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Q1. If a car travels 100 meters in 5 seconds, what is its average speed?

Solution:

Average speed is calculated as total distance divided by total time: 100 m / 5 s = 20 m/s.

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Q2. If a ball is thrown vertically upward with an initial velocity of 15 m/s, how high will it go before coming to a stop?

Solution:

Using the formula h = v²/(2g), where v = 15 m/s and g = 9.81 m/s², we find h = (15)²/(2*9.81) ≈ 11.47 m.

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Q3. What is the time taken for an object to fall from a height of 45 m under gravity?

Solution:

Using the formula h = 0.5 * g * t², we can rearrange to find t = √(2h/g). Substituting h = 45 m and g = 9.81 m/s² gives t ≈ 4.5 s.

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Q4. If a car accelerates from rest at a rate of 2 m/s², what is its velocity after 5 seconds?

Solution:

Using the formula v = u + at, where u = 0, a = 2 m/s², and t = 5 s, we get v = 0 + (2)(5) = 10 m/s.

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Q5. A 2 kg object is moving with a velocity of 3 m/s. What is its kinetic energy?

Solution:

Kinetic energy is given by KE = 0.5 * m * v² = 0.5 * 2 kg * (3 m/s)² = 9 J.

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Q6. What is the center of gravity of a uniform beam of length L?

Solution:

For a uniform beam, the center of gravity is located at its midpoint, which is L/2.

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Q7. An object is thrown horizontally from a height of 45 m. How long does it take to hit the ground? (g = 9.8 m/s²)

Solution:

Using the formula s = 0.5gt², we have 45 = 0.5 * 9.8 * t², solving gives t ≈ 3.03 s.

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Q8. An object is in free fall from a height of 80 m. How long will it take to reach the ground? (g = 9.8 m/s²)

Solution:

Using the formula s = ut + 0.5gt², where u = 0, s = 80 m, and g = 9.8 m/s², we solve 80 = 0 + 0.5 * 9.8 * t², giving t ≈ 4.04 s.

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Q9. A force of 50 N is applied at an angle of 30 degrees to the horizontal. What is the horizontal component of the force?

Solution:

The horizontal component is given by F_horizontal = F * cos(θ) = 50 N * cos(30°) = 50 N * (√3/2) ≈ 43.3 N.

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Q10. What is the formula for calculating the frictional force?

Solution:

The frictional force is calculated using the formula F_friction = μN, where μ is the coefficient of friction and N is the normal force.