Kinematics
Q. A train leaves a station at 80 km/h and another train leaves the same station 30 minutes later at 100 km/h. How far from the station will they meet?
A.
100 km
B.
120 km
C.
150 km
D.
180 km
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Solution
Let the time taken by the first train be t hours. Distance = speed * time. 80t = 100(t - 0.5). Solving gives t = 2 hours, so distance = 80 * 2 = 160 km.
Correct Answer: B — 120 km
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Q. A train moving at 72 km/h overtakes a man walking at 6 km/h in the same direction. How fast does the train appear to be moving to the man?
A.
66 km/h
B.
72 km/h
C.
78 km/h
D.
84 km/h
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Solution
Relative speed = Speed of train - Speed of man = 72 km/h - 6 km/h = 66 km/h.
Correct Answer: A — 66 km/h
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Q. A train moving at 72 km/h passes a man walking at 6 km/h in the same direction. How fast does the train appear to be moving to the man?
A.
66 km/h
B.
72 km/h
C.
78 km/h
D.
84 km/h
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Solution
Relative speed = Speed of train - Speed of man = 72 km/h - 6 km/h = 66 km/h.
Correct Answer: A — 66 km/h
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Q. A train moving at 72 km/h passes a platform 300 m long. How long does it take to cross the platform completely?
A.
10 seconds
B.
15 seconds
C.
20 seconds
D.
25 seconds
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Solution
Total distance = Length of train + Length of platform. If length of train is L, time = (L + 300)/20 m/s. Assuming L = 300 m, time = (300 + 300)/20 = 30 seconds.
Correct Answer: B — 15 seconds
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Q. A train moving at a speed of 72 km/h applies brakes and comes to a stop in 5 seconds. What is the acceleration of the train?
A.
-4 m/s²
B.
-2 m/s²
C.
-3 m/s²
D.
-1 m/s²
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Solution
First, convert speed to m/s: 72 km/h = 20 m/s. Using a = (v - u)/t = (0 - 20)/5 = -4 m/s².
Correct Answer: A — -4 m/s²
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Q. A train moving with a speed of 60 km/h applies brakes and comes to a stop in 5 seconds. What is the magnitude of its acceleration?
A.
-3 m/s²
B.
-2 m/s²
C.
-1 m/s²
D.
-4 m/s²
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Solution
First, convert speed to m/s: 60 km/h = 60/3.6 = 16.67 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately -3 m/s².
Correct Answer: A — -3 m/s²
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Q. A train moving with a speed of 72 km/h applies brakes and comes to a stop in 10 seconds. What is the acceleration of the train?
A.
-2 m/s²
B.
-3 m/s²
C.
-4 m/s²
D.
-5 m/s²
Show solution
Solution
First convert speed to m/s: 72 km/h = 20 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 20) / 10 = -2 m/s².
Correct Answer: B — -3 m/s²
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Q. A train moving with a speed of 72 km/h applies brakes and comes to a stop in 10 seconds. What is the magnitude of its acceleration?
A.
-2 m/s²
B.
-3 m/s²
C.
-4 m/s²
D.
-5 m/s²
Show solution
Solution
First convert speed to m/s: 72 km/h = 20 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 20) / 10 = -2 m/s².
Correct Answer: C — -4 m/s²
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Q. A train travels 120 km at a uniform speed. If it takes 2 hours to complete the journey, what is the speed of the train?
A.
50 km/h
B.
60 km/h
C.
70 km/h
D.
80 km/h
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Solution
Speed = distance / time = 120 km / 2 h = 60 km/h.
Correct Answer: B — 60 km/h
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Q. A train travels at a speed of 72 km/h. How far will it travel in 30 minutes?
A.
12 km
B.
18 km
C.
24 km
D.
36 km
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Solution
Distance = speed × time = 72 km/h × 0.5 h = 36 km.
Correct Answer: B — 18 km
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Q. A train travels at a speed of 72 km/h. How long will it take to cover a distance of 180 km?
A.
2 hours
B.
2.5 hours
C.
3 hours
D.
3.5 hours
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Solution
Time = distance / speed. Convert speed to m/s: 72 km/h = 20 m/s. Time = 180 km / 72 km/h = 2.5 hours.
Correct Answer: C — 3 hours
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Q. A train travels at a speed of 90 km/h and a car at 60 km/h. If they start from the same point and travel in the same direction, how far apart will they be after 1 hour?
A.
30 km
B.
20 km
C.
10 km
D.
40 km
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Solution
Relative speed = 90 - 60 = 30 km/h. Distance apart after 1 hour = 30 km.
Correct Answer: A — 30 km
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Q. A vehicle moving with a speed of 60 km/h applies brakes and comes to a stop in 5 seconds. What is the deceleration?
A.
2 m/s²
B.
3 m/s²
C.
4 m/s²
D.
5 m/s²
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Solution
Convert speed to m/s: 60 km/h = 16.67 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately 3 m/s².
Correct Answer: B — 3 m/s²
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Q. An object is dropped from a height of 80 m. How long will it take to reach the ground?
A.
4 s
B.
5 s
C.
6 s
D.
8 s
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Solution
Using the formula: h = 0.5 * g * t², where h = 80 m and g = 9.8 m/s². Solving for t gives t = sqrt(2h/g) = sqrt(2*80/9.8) ≈ 4.04 s, approximately 4 s.
Correct Answer: B — 5 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 = 10 m/s²)
A.
4 s
B.
5 s
C.
6 s
D.
8 s
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Solution
Using the formula: h = 0.5 * g * t². 80 = 0.5 * 10 * t². Solving gives t² = 16, so t = 4 s.
Correct Answer: B — 5 s
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Q. An object is moving in a circular path with a radius of 10 m at a speed of 5 m/s. What is the period of the motion?
A.
2π s
B.
4π s
C.
10 s
D.
20 s
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Solution
Period (T) = 2πr/v = 2π(10)/5 = 4π s.
Correct Answer: A — 2π s
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Q. An object is projected at an angle of 60 degrees with an initial speed of 30 m/s. What is the horizontal component of its velocity?
A.
15 m/s
B.
25 m/s
C.
30 m/s
D.
20 m/s
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Solution
Horizontal component (v_x) = u * cos(θ) = 30 * (1/2) = 15 m/s.
Correct Answer: B — 25 m/s
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Q. An object is projected at an angle of 60 degrees with an initial speed of 30 m/s. What is the vertical component of its velocity?
A.
15 m/s
B.
25 m/s
C.
30 m/s
D.
20 m/s
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Solution
Vertical component (v_y) = u * sin(θ) = 30 * (√3/2) = 25.98 m/s.
Correct Answer: B — 25 m/s
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Q. An object is projected at an angle of 60 degrees with an initial velocity of 30 m/s. What is the time of flight?
A.
3 s
B.
5 s
C.
6 s
D.
10 s
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Solution
Time of flight (T) = (2u * sin(θ)) / g = (2 * 30 * √3/2) / 9.8 = 5.18 s.
Correct Answer: C — 6 s
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Q. An object is projected at an angle of 60 degrees with an initial velocity of 30 m/s. What is the horizontal component of its velocity?
A.
15 m/s
B.
25 m/s
C.
30 m/s
D.
20 m/s
Show solution
Solution
Horizontal component Vx = u * cos(θ) = 30 * (1/2) = 15 m/s.
Correct Answer: B — 25 m/s
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Q. An object is thrown at an angle of 30 degrees with a speed of 40 m/s. What is the time of flight until it returns to the same vertical level?
A.
4 s
B.
5 s
C.
6 s
D.
8 s
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Solution
Time of flight (T) = (2 * u * sin(θ)) / g = (2 * 40 * 0.5) / 9.8 ≈ 4.08 s.
Correct Answer: C — 6 s
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Q. An object is thrown horizontally from the top of a 45 m high cliff. How far from the base of the cliff will it land if the initial speed is 10 m/s?
A.
10 m
B.
20 m
C.
30 m
D.
40 m
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Solution
Time of flight (t) = √(2h/g) = √(2*45/9.8) = 3.03 s. Horizontal distance = speed * time = 10 * 3.03 = 30.3 m.
Correct Answer: B — 20 m
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Q. An object is thrown horizontally from the top of a 45 m high cliff. How far from the base of the cliff will it land if it is thrown with a speed of 10 m/s?
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Show solution
Solution
Time of flight (t) = √(2h/g) = √(2*45/9.8) = 3.03 s. Horizontal distance = speed * time = 10 * 3.03 = 30.3 m.
Correct Answer: B — 30 m
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Q. An object is thrown horizontally from the top of a cliff 80 m high. How long does it take to hit the ground?
A.
2 s
B.
4 s
C.
5 s
D.
8 s
Show solution
Solution
Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.
Correct Answer: B — 4 s
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Q. An object is thrown horizontally from the top of a cliff of height 80 m. How long does it take to hit the ground?
A.
2 s
B.
4 s
C.
5 s
D.
8 s
Show solution
Solution
Using h = (1/2)gt^2, we have 80 = (1/2)(9.8)t^2, solving gives t ≈ 4 s.
Correct Answer: B — 4 s
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Q. An object is thrown horizontally from the top of a tower 80 m high. How long will it take to hit the ground?
A.
4 s
B.
5 s
C.
3 s
D.
2 s
Show solution
Solution
Using the equation h = (1/2)gt², where h = 80 m and g = 9.8 m/s², we have 80 = (1/2)*9.8*t². Solving gives t² = 16.33, so t ≈ 4 s.
Correct Answer: B — 5 s
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Q. An object is thrown upwards with a speed of 20 m/s. How long will it take to reach the maximum height? (Assume g = 10 m/s²)
A.
1 s
B.
2 s
C.
3 s
D.
4 s
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Solution
Time to reach maximum height = initial velocity / g = 20 m/s / 10 m/s² = 2 s.
Correct Answer: B — 2 s
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Q. An object is thrown vertically upward with a speed of 20 m/s. How high will it rise before coming to rest?
A.
10 m
B.
20 m
C.
30 m
D.
40 m
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Solution
Maximum height (H) = (u²)/(2g) = (20²)/(2*9.8) ≈ 20.4 m.
Correct Answer: C — 30 m
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Q. An object is thrown vertically upward with a speed of 30 m/s. How high will it rise before coming to rest?
A.
45 m
B.
90 m
C.
135 m
D.
180 m
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Solution
Using the formula: h = (v² - u²) / (2g), where v = 0 m/s, u = 30 m/s, g = 9.8 m/s². h = (0 - 30²) / (2 * -9.8) = 45.92 m, approximately 45 m.
Correct Answer: B — 90 m
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Q. An object is thrown vertically upward with a speed of 30 m/s. How high will it rise before coming to a momentary stop?
A.
45 m
B.
60 m
C.
90 m
D.
135 m
Show solution
Solution
Using the formula: h = (v² - u²) / (2g), where v = 0 m/s (at the highest point), u = 30 m/s, g = 9.8 m/s². h = (0 - 30²) / (2 * -9.8) = 45.92 m, approximately 45 m.
Correct Answer: B — 60 m
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