Kinematics
Q. A boat can travel at a speed of 10 km/h in still water. If the speed of the current is 2 km/h, what is the speed of the boat downstream?
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
14 km/h
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Solution
Speed downstream = speed of boat + speed of current = 10 + 2 = 12 km/h.
Correct Answer: C — 12 km/h
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Q. A boat is moving upstream at 10 km/h in a river that flows at 5 km/h. What is the speed of the boat relative to the riverbank?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
0 km/h
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Solution
Speed of boat relative to riverbank = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.
Correct Answer: C — 15 km/h
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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the ground?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
20 km/h
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Solution
Speed of boat relative to ground = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.
Correct Answer: A — 5 km/h
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Q. A boat is moving upstream at 10 km/h in a river that flows downstream at 5 km/h. What is the speed of the boat relative to the riverbank?
A.
5 km/h
B.
10 km/h
C.
15 km/h
D.
20 km/h
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Solution
Speed of boat relative to riverbank = Speed of boat - Speed of river = 10 km/h - 5 km/h = 5 km/h.
Correct Answer: A — 5 km/h
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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the boat in still water if the speed of the current is 5 km/h?
A.
10 km/h
B.
15 km/h
C.
20 km/h
D.
25 km/h
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Solution
Speed downstream = distance/time = 30/2 = 15 km/h. Speed of boat in still water = speed downstream - speed of current = 15 - 5 = 10 km/h.
Correct Answer: B — 15 km/h
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Q. A boat travels 30 km downstream in 2 hours. What is the speed of the current if the speed of the boat in still water is 15 km/h?
A.
2.5 km/h
B.
5 km/h
C.
7.5 km/h
D.
10 km/h
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Solution
Speed downstream = distance/time = 30/2 = 15 km/h. Speed of current = speed downstream - speed of boat = 15 - 15 = 0 km/h.
Correct Answer: B — 5 km/h
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Q. A boat travels 30 km upstream and 30 km downstream in a total time of 6 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?
A.
2 km/h
B.
3 km/h
C.
4 km/h
D.
5 km/h
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Solution
Let speed of current = x. Time upstream = 30/(10-x), downstream = 30/(10+x). Total time = 6 hours. Solving gives x = 2 km/h.
Correct Answer: A — 2 km/h
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Q. A boat travels across a river with a speed of 4 m/s relative to the water. If the river flows at 3 m/s, what is the resultant speed of the boat relative to the riverbank?
A.
3 m/s
B.
4 m/s
C.
5 m/s
D.
7 m/s
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Solution
Resultant speed = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 m/s.
Correct Answer: C — 5 m/s
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Q. A boat travels across a river with a speed of 8 km/h relative to the water. If the river flows at 6 km/h, what is the speed of the boat relative to the riverbank?
A.
8 km/h
B.
10 km/h
C.
14 km/h
D.
6 km/h
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Solution
Speed of boat relative to riverbank = √(8^2 + 6^2) = √(64 + 36) = √100 = 10 km/h.
Correct Answer: B — 10 km/h
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Q. A boat travels upstream at 4 km/h and downstream at 6 km/h. What is the speed of the current?
A.
1 km/h
B.
2 km/h
C.
3 km/h
D.
4 km/h
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Solution
Let the speed of the current be x. Then, 4 + x = 6 - x. Solving gives x = 2 km/h.
Correct Answer: B — 2 km/h
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Q. A body moves in a straight line with a uniform acceleration of 2 m/s². If its initial velocity is 5 m/s, what will be its velocity after 10 seconds?
A.
25 m/s
B.
20 m/s
C.
15 m/s
D.
10 m/s
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Solution
Final velocity = initial velocity + acceleration * time = 5 + 2 * 10 = 25 m/s.
Correct Answer: A — 25 m/s
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Q. A body moves in a straight line with an initial velocity of 10 m/s and accelerates at 2 m/s². What will be its velocity after 5 seconds?
A.
20 m/s
B.
25 m/s
C.
30 m/s
D.
35 m/s
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Solution
Final velocity (v) = u + at = 10 + 2*5 = 20 m/s.
Correct Answer: C — 30 m/s
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Q. A body moving with a uniform speed of 10 m/s covers a distance of 100 m. How much time does it take?
A.
5 s
B.
10 s
C.
15 s
D.
20 s
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Solution
Time = distance / speed = 100 m / 10 m/s = 10 s.
Correct Answer: B — 10 s
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Q. A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
A.
100 m
B.
200 m
C.
300 m
D.
400 m
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Solution
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. Here, initial velocity = 0, final velocity = 20 m/s, time = 10 s. Acceleration = (final velocity - initial velocity) / time = 2 m/s². Distance = 0 + 0.5 * 2 * 10² = 100 m.
Correct Answer: B — 200 m
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Q. A car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds. What is the distance covered by the car during this time?
A.
100 m
B.
125 m
C.
150 m
D.
200 m
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Solution
Distance (s) = ut + (1/2)at^2. Here, a = (v-u)/t = (25-0)/10 = 2.5 m/s². So, s = 0 + (1/2)*2.5*10^2 = 125 m.
Correct Answer: B — 125 m
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Q. A car is moving at 80 km/h and a motorcycle at 60 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.
20 km/h
B.
60 km/h
C.
80 km/h
D.
140 km/h
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Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind).
Correct Answer: A — 20 km/h
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Q. A car is moving at 80 km/h and a motorcycle is moving at 100 km/h in the same direction. What is the speed of the motorcycle relative to the car?
A.
20 km/h
B.
80 km/h
C.
100 km/h
D.
180 km/h
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Solution
Relative speed = Speed of motorcycle - Speed of car = 100 km/h - 80 km/h = 20 km/h.
Correct Answer: A — 20 km/h
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Q. A car is moving at 80 km/h and a motorcycle is moving at 100 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.
20 km/h
B.
180 km/h
C.
100 km/h
D.
80 km/h
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Solution
Relative speed = Speed of motorcycle - Speed of car = 100 km/h - 80 km/h = 20 km/h.
Correct Answer: A — 20 km/h
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Q. A car is moving at 80 km/h and a motorcycle is moving at 60 km/h in the same direction. What is the speed of the motorcycle relative to the car?
A.
20 km/h
B.
60 km/h
C.
80 km/h
D.
140 km/h
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Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind the car).
Correct Answer: A — 20 km/h
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Q. A car is moving at 80 km/h and a motorcycle is moving at 60 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.
20 km/h
B.
60 km/h
C.
80 km/h
D.
140 km/h
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Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind).
Correct Answer: A — 20 km/h
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Q. A car moves in a circular path of radius 50 m at a constant speed of 20 m/s. What is the centripetal acceleration?
A.
4 m/s²
B.
8 m/s²
C.
10 m/s²
D.
16 m/s²
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Solution
Centripetal acceleration (a_c) = v²/r = (20²)/50 = 8 m/s².
Correct Answer: C — 10 m/s²
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Q. A car moves in a circular path of radius 50 m with a constant speed of 20 m/s. What is the centripetal acceleration?
A.
4 m/s²
B.
8 m/s²
C.
10 m/s²
D.
16 m/s²
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Solution
Centripetal acceleration (a_c) = v²/r = (20²)/50 = 8 m/s².
Correct Answer: C — 10 m/s²
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Q. A car moving with a speed of 30 m/s applies brakes and comes to a stop in 5 seconds. What is the deceleration of the car?
A.
3 m/s²
B.
4 m/s²
C.
5 m/s²
D.
6 m/s²
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Solution
Deceleration = (final velocity - initial velocity) / time = (0 - 30) / 5 = -6 m/s².
Correct Answer: A — 3 m/s²
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Q. A car travels 100 m in 4 seconds. What is its average speed?
A.
20 m/s
B.
25 m/s
C.
30 m/s
D.
35 m/s
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Solution
Average speed = total distance / total time = 100 m / 4 s = 25 m/s.
Correct Answer: B — 25 m/s
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Q. A car travels 100 m in 5 seconds. What is its average speed?
A.
20 m/s
B.
25 m/s
C.
15 m/s
D.
30 m/s
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Solution
Average speed = total distance / total time = 100 m / 5 s = 20 m/s.
Correct Answer: B — 25 m/s
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Q. A car travels 100 m north and then 100 m east. What is the magnitude of the displacement from the starting point? (2000)
A.
100 m
B.
141.42 m
C.
200 m
D.
50 m
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Solution
Displacement = √(100^2 + 100^2) = √20000 = 141.42 m.
Correct Answer: B — 141.42 m
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Q. A car travels at 90 km/h and a truck at 60 km/h in opposite directions. What is the relative speed of the car with respect to the truck?
A.
30 km/h
B.
60 km/h
C.
150 km/h
D.
90 km/h
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Solution
Relative speed = Speed of car + Speed of truck = 90 km/h + 60 km/h = 150 km/h.
Correct Answer: C — 150 km/h
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Q. A car travels at a speed of 80 km/h and a bike travels 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.
20 km
B.
10 km
C.
30 km
D.
40 km
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Solution
Relative speed = 80 - 60 = 20 km/h. Distance apart after 1 hour = 20 km.
Correct Answer: A — 20 km
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Q. A car travels at a speed of 80 km/h and a truck travels at 60 km/h in the same direction. How far apart will they be after 2 hours if they start together?
A.
20 km
B.
40 km
C.
60 km
D.
80 km
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Solution
Relative speed = 80 - 60 = 20 km/h. Distance = speed * time = 20 * 2 = 40 km.
Correct Answer: B — 40 km
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Q. A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 10 seconds?
A.
50 m
B.
100 m
C.
150 m
D.
200 m
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Solution
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 10² = 50 m.
Correct Answer: B — 100 m
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