Mechanics - Kinematics

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Q1. A stone is thrown downward with an initial velocity of 5 m/s from a height of 45 m. How long will it take to hit the ground? (2020)

Solution:

Using the equation of motion: h = ut + 0.5gt². Solving for t gives t ≈ 4 seconds.

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Q2. A cyclist travels at a speed of 10 m/s for 15 seconds. What distance does he cover? (2022)

Solution:

Distance = speed * time = 10 m/s * 15 s = 150 m.

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Q3. A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height it reaches? (2022)

Solution:

Using the formula: H = (u² * sin²θ) / (2g). H = (20² * (1/2)) / (2 * 9.8) = 10.2 m, approximately 10 m.

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Q4. A car moving at 15 m/s comes to a stop in 5 seconds. What is its acceleration? (2019)

Solution:

Using the formula: acceleration = (final velocity - initial velocity) / time. Acceleration = (0 - 15) / 5 = -3 m/s².

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Q5. An object moves with a uniform speed of 5 m/s. How far will it travel in 20 seconds? (2023)

Solution:

Distance = speed * time = 5 m/s * 20 s = 100 m.

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Q6. A train starts from rest and accelerates uniformly at 2 m/s². What is its speed after 10 seconds? (2021)

Solution:

Using the formula: final velocity = initial velocity + acceleration * time. Final velocity = 0 + 2 * 10 = 20 m/s.