ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Motion, Force and Momentum (Set 2): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review.…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A cyclist's speed rises steadily from 4 m/s to 12 m/s over 8 s. What distance does she cover meanwhile?
Answer: A. 64 m
Explanation: s = ½(u + v)t = ½(4 + 12)(8) = 64 m.
Q2. A body starts from rest with uniform acceleration and covers 15 m during the 3rd second of its motion. What is its acceleration?
Answer: A. 6 m/s²
Explanation: Distance in the nth second = a(n − ½) for u = 0: 15 = a(2.5), so a = 6 m/s².
Q3. A ball is thrown vertically upward at 30 m/s. What is its velocity 4 s later? (g = 10 m/s²)
Answer: D. 10 m/s downward
Explanation: v = u − gt = 30 − 40 = -10 m/s; the negative sign means 10 m/s downward.
Q4. A stone is dropped from rest from the top of an 80 m tower. How long does it take to reach the ground? (g = 10 m/s²)
Answer: D. 4 s
Explanation: h = ½gt² gives t = √(2h/g) = √16 = 4 s.
Q5. A velocity–time graph is a straight line falling from 20 m/s at t = 0 to zero at t = 4 s. What displacement does it represent?
Answer: A. 40 m
Explanation: Displacement = area under the v–t graph = ½ × 4 × 20 = 40 m.
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Q6. Two cars 140 m apart move towards each other on a straight road at 20 m/s and 15 m/s. After how long do they meet?
Q7. A swimmer can swim at 5 m/s in still water and wants to reach the point directly opposite on the other bank of a 120 m wide stream flowing at 3 m/s. She aims partly upstream. How long does the crossing take?
Q8. A footballer kicks a ball with a velocity of 30 m/s directed 30° above the ground. How high does the ball rise? (g = 10 m/s²)
Q9. A ball is kicked at 20 m/s at 15° above the horizontal. What is its horizontal range? (g = 10 m/s²)
Q10. A projectile is launched at 60° above the horizontal. What is the ratio of its kinetic energy at the highest point to its kinetic energy at launch?
Q11. A ball is thrown horizontally at 15 m/s from a height of 20 m. With what speed does it hit the ground? (g = 10 m/s²)
Q12. Two balls are projected with the same speed at 30° and 60° to the horizontal. What is the ratio of their maximum heights?
Q13. A 10 kg box is pulled across a floor by a horizontal force of 50 N against a friction force of 20 N. What is its acceleration?
Q14. A block slides down a smooth plane inclined at 30° to the horizontal. What is its acceleration? (g = 10 m/s²)
Q15. A block slides down a rough plane inclined at 30°. The coefficient of kinetic friction is 1/(2√3). What is its acceleration? (g = 10 m/s²)
Q16. A 50 kg girl stands on a weighing machine in a lift that is moving upward but slowing down at 2 m/s². What does the machine read? (g = 10 m/s²)
Q17. Masses of 5 kg and 3 kg hang from the ends of a light string over a frictionless pulley. What is the acceleration of the system? (g = 10 m/s²)
Q18. A 4 kg trolley on a level frictionless track is pulled by a cord that runs over a pulley and supports a hanging 1 kg mass. What is the tension in the cord while they move? (g = 10 m/s²)
Q19. What is the momentum of a 2000 kg car travelling at 72 km/h?
Q20. A 3 kg body at rest explodes into two pieces of 1 kg and 2 kg. The 1 kg piece flies off at 12 m/s. What is the speed of the 2 kg piece?
Q21. A body at rest explodes into fragments of 1 kg and 2 kg; the 1 kg fragment moves at 12 m/s. How much kinetic energy is released in the explosion?
Q22. A 2 kg ball moving at 3 m/s makes a head-on elastic collision with a 1 kg ball at rest. What are their velocities after the collision?
Q23. A 10 g bullet moving at 500 m/s embeds itself in a 2.49 kg wooden block resting on a smooth surface. What is the speed of the block just afterwards?
Q24. The force on a ball during a kick rises uniformly from 0 to 100 N and falls back uniformly to 0, the whole contact lasting 0.02 s. What impulse does the ball receive?
Q25. A fielder moves his hands backward while catching a fast cricket ball. This reduces the force on his hands because it:
Q26. Standing passengers lurch forward when a bus brakes suddenly. This is explained by:
Q27. An athlete runs exactly one lap of a 400 m circular track in 50 s, finishing where she started. What are her average speed and average velocity?
Q28. A 1000 kg rocket ejects gases at 2000 m/s relative to it. At what rate must it eject gas so that the thrust just balances its weight at lift-off? (g = 10 m/s²)
Q29. A 2 kg body falls freely from rest through 5 m. What is its momentum just before it hits the ground? (g = 10 m/s²)
Q30. The position of a particle moving along the x-axis is x = 3t² + 2t (x in metres, t in seconds). What is its acceleration?