Motion in a Plane

Q. A boat can travel at a speed of 20 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Let the speed of the current be x km/h. Upstream speed = 20 - x, Downstream speed = 20 + x. Time upstream = 2 hours, Time downstream = 1 hour. Distance = (20 - x) * 2 = (20 + x) * 1. Solving gives x = 5 km/h.

Correct Answer: A — 5 km/h

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Q. A car accelerates from rest at a rate of 2 m/s². How far does it travel in 10 seconds?

A. 50 m
B. 100 m
C. 150 m
D. 200 m

Solution

Distance = 0.5 * acceleration * time² = 0.5 * 2 m/s² * (10 s)² = 100 m.

Correct Answer: B — 100 m

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Q. A car travels 60 km in 1 hour and then 90 km in 1.5 hours. What is the average speed of the car for the entire journey?

A. 50 km/h
B. 60 km/h
C. 70 km/h
D. 80 km/h

Solution

Total distance = 60 km + 90 km = 150 km. Total time = 1 hour + 1.5 hours = 2.5 hours. Average speed = Total distance / Total time = 150 km / 2.5 hours = 60 km/h.

Correct Answer: B — 60 km/h

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Q. A cyclist travels 30 km at a speed of 15 km/h. How long does it take to complete the journey?

A. 1 hour
B. 2 hours
C. 2.5 hours
D. 3 hours

Solution

Time = Distance / Speed = 30 km / 15 km/h = 2 hours.

Correct Answer: B — 2 hours

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Q. A person walks 4 km north and then 3 km east. What is the straight-line distance from the starting point to the endpoint?

A. 5 km
B. 6 km
C. 7 km
D. 8 km

Solution

Using Pythagoras theorem, Distance = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 km.

Correct Answer: A — 5 km

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Q. A plane flies from City A to City B, a distance of 1200 km, at a speed of 400 km/h. How long does the flight take?

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

Solution

Time = Distance / Speed = 1200 km / 400 km/h = 3 hours.

Correct Answer: C — 4 hours

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Q. A runner completes a 400 m lap in 50 seconds. What is the runner's speed in m/s?

A. 6 m/s
B. 7 m/s
C. 8 m/s
D. 9 m/s

Solution

Speed = Distance / Time = 400 m / 50 s = 8 m/s.

Correct Answer: A — 6 m/s

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Q. A vehicle travels 120 km in 2 hours and then 180 km in 3 hours. What is the overall average speed?

A. 60 km/h
B. 70 km/h
C. 80 km/h
D. 90 km/h

Solution

Total distance = 120 km + 180 km = 300 km. Total time = 2 hours + 3 hours = 5 hours. Average speed = Total distance / Total time = 300 km / 5 hours = 60 km/h.

Correct Answer: B — 70 km/h

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Q. If a train travels 180 km at a speed of 90 km/h, how long does the journey take?

A. 1 hour
B. 2 hours
C. 2.5 hours
D. 3 hours

Solution

Time = Distance / Speed = 180 km / 90 km/h = 2 hours.

Correct Answer: B — 2 hours

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Q. Two trains are moving towards each other at speeds of 60 km/h and 90 km/h. If they are 300 km apart, how long will they take to meet?

A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours

Solution

Relative speed = 60 km/h + 90 km/h = 150 km/h. Time = Distance / Speed = 300 km / 150 km/h = 2 hours.

Correct Answer: C — 3 hours

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Motion in a Plane

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