Q1. A car moving at 60 km/h applies brakes and comes to a stop in 5 seconds. What is the distance covered during braking?
Solution:
Convert speed to m/s: 60 km/h = 16.67 m/s. Using s = ut + 0.5at², where a = (0 - 16.67)/5 = -3.33 m/s², we find s = 16.67 * 5 + 0.5 * (-3.33) * 5² = 41.67 m.
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Q2. A cyclist travels at a speed of 15 m/s. How long will it take to cover a distance of 300 meters?
Solution:
Using the formula time = distance/speed, we have time = 300 m / 15 m/s = 20 s.
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Q3. 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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Q4. If a car accelerates from rest at a rate of 3 m/s², what is its velocity after 5 seconds?
Solution:
Using the formula v = u + at, where u = 0, a = 3 m/s², and t = 5 s, we get v = 0 + (3)(5) = 15 m/s.
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Q5. In a frictionless environment, if a 5 kg block is pushed with a force of 20 N, what will be its acceleration?
Solution:
Using F = ma, we have 20 N = 5 kg * a, thus a = 20 N / 5 kg = 4 m/s².
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Q6. 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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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. A ball is thrown vertically upwards with a speed of 20 m/s. How high will it go before it starts to fall back down? (g = 10 m/s²)
Solution:
Using the formula v² = u² + 2as, where v = 0, u = 20 m/s, and a = -10 m/s², we get 0 = 20² + 2 * (-10) * s, solving gives s = 20 m.
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Q9. 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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Q10. What is the acceleration of an object in free fall near the Earth's surface?
Solution:
The acceleration due to gravity near the Earth's surface is approximately 9.81 m/s².
