Kinematics: Motion in One Dimension for Competitive Exams

Kinematics: Motion in One Dimension

Q. A ball is dropped from a height of 45 meters. How long will it take to hit the ground? (Assume g = 9.8 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.06 s.

Correct Answer: C — 4 s

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Q. A ball is thrown horizontally from a height of 45 m. How long does it take to hit the ground? (Assume g = 9.8 m/s²)

A. 2 s
B. 3 s
C. 4 s
D. 5 s

Solution

Using the formula t = √(2h/g), where h = 45 m and g = 9.8 m/s², we get t = √(2 * 45 / 9.8) ≈ 3.03 s.

Correct Answer: C — 4 s

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Q. A cyclist accelerates from rest to a speed of 15 m/s in 10 seconds. What is the cyclist's acceleration?

A. 1.5 m/s²
B. 2 m/s²
C. 3 m/s²
D. 4 m/s²

Solution

Acceleration = (final velocity - initial velocity) / time = (15 m/s - 0) / 10 s = 1.5 m/s².

Correct Answer: B — 2 m/s²

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Q. A cyclist travels 100 meters in 5 seconds. What is the average speed of the cyclist?

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Average speed = total distance / total time = 100 m / 5 s = 20 m/s.

Correct Answer: A — 10 m/s

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Q. A runner accelerates from rest to a speed of 10 m/s in 5 seconds. What is the total distance covered during this time?

A. 12.5 m
B. 25 m
C. 50 m
D. 100 m

Solution

Using the formula d = 0.5 * a * t², first find a = (v_f - v_i) / t = (10 - 0) / 5 = 2 m/s². Then, d = 0.5 * 2 * (5)² = 25 m.

Correct Answer: A — 12.5 m

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Q. A runner completes a 400 m lap in 50 seconds. What is their average speed?

A. 6 m/s
B. 8 m/s
C. 10 m/s
D. 12 m/s

Solution

Average speed = total distance / total time = 400 m / 50 s = 8 m/s.

Correct Answer: B — 8 m/s

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Q. A stone is thrown horizontally from a height of 20 meters. How long does it take to hit the ground? (Assume g = 9.8 m/s²)

A. 1 s
B. 2 s
C. 3 s
D. 4 s

Solution

Using the formula t = √(2h/g), where h = 20 m and g = 9.8 m/s², we get t = √(2 * 20 / 9.8) ≈ 2.02 s.

Correct Answer: B — 2 s

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Q. A stone is thrown straight up with a speed of 30 m/s. How long will it take to reach its highest point? (Assume g = 9.8 m/s²)

A. 1.5 s
B. 2 s
C. 3 s
D. 4 s

Solution

Time to reach the highest point is given by t = v/g, where v = 30 m/s and g = 9.8 m/s², so t = 30 / 9.8 ≈ 3.06 s.

Correct Answer: B — 2 s

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Q. A train is moving with a velocity of 80 m/s and comes to a stop in 10 seconds. What is the acceleration of the train?

A. -8 m/s²
B. -4 m/s²
C. 0 m/s²
D. 8 m/s²

Solution

Using the formula a = (v_f - v_i) / t, where v_f = 0 m/s, v_i = 80 m/s, and t = 10 s, we get a = (0 - 80) / 10 = -8 m/s².

Correct Answer: A — -8 m/s²

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Q. A train moving at 72 km/h comes to a stop in 5 seconds. What is the train's deceleration?

A. 2 m/s²
B. 3 m/s²
C. 4 m/s²
D. 5 m/s²

Solution

First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².

Correct Answer: C — 4 m/s²

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Q. A vehicle travels 150 meters in 10 seconds. What is its average velocity?

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Average velocity = total distance / total time = 150 m / 10 s = 15 m/s.

Correct Answer: B — 15 m/s

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Q. An object is dropped from a height of 80 m. How long will it take to reach the ground? (Assume g = 9.8 m/s²)

A. 2 s
B. 4 s
C. 6 s
D. 8 s

Solution

Using the formula t = √(2h/g), where h = 80 m and g = 9.8 m/s², we get t = √(2 * 80 / 9.8) ≈ 4.04 s.

Correct Answer: C — 6 s

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Q. An object is thrown vertically upward with an initial velocity of 20 m/s. How high will it go before coming to a stop?

A. 10 m
B. 20 m
C. 40 m
D. 50 m

Solution

Using the formula h = (v²)/(2g), where v = 20 m/s and g = 9.8 m/s², we get h = (20)²/(2 * 9.8) ≈ 20.4 m.

Correct Answer: C — 40 m

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Q. An object moves in a straight line with a constant acceleration of 3 m/s². If its initial velocity is 5 m/s, what will be its velocity after 4 seconds?

A. 5 m/s
B. 11 m/s
C. 17 m/s
D. 23 m/s

Solution

Using the formula v = v_i + at, where v_i = 5 m/s, a = 3 m/s², and t = 4 s, we get v = 5 + (3 * 4) = 17 m/s.

Correct Answer: C — 17 m/s

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Q. An object moves with a constant acceleration of 3 m/s². If it starts from rest, what is its velocity after 4 seconds?

A. 6 m/s
B. 9 m/s
C. 12 m/s
D. 15 m/s

Solution

Using the formula v = u + at, where u = 0, a = 3 m/s², and t = 4 s, we get v = 0 + 3 * 4 = 12 m/s.

Correct Answer: C — 12 m/s

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Q. If a car is moving at a constant speed of 60 km/h, how far will it travel in 2 hours?

A. 60 km
B. 120 km
C. 180 km
D. 240 km

Solution

Distance = speed × time = 60 km/h × 2 h = 120 km.

Correct Answer: B — 120 km

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Kinematics: Motion in One Dimension

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