ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Motion, Force and Momentum (Set 6): 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 driver travelling at 20 m/s sees an obstacle, reacts after 0.6 s (during which the speed stays constant) and then brakes with a uniform deceleration of 8 m/s². The total distance travelled from the moment of seeing the obstacle until stopping is
Answer: B. 37 m
Explanation: Reaction: 20×0.6 = 12 m. Braking: 20²/(2×8) = 25 m. Total = 37 m.
Q2. A car A moves past a point at a constant 20 m/s. At that instant a car B, at the same point, starts from rest with a constant acceleration of 2 m/s² in the same direction. How far from the point does B catch A?
Answer: D. 400 m
Explanation: Equal displacements: 20t = ½(2)t², so t = 20 s and the distance is 20×20 = 400 m.
Q3. A velocity–time graph is a straight line rising from 0 to 12 m/s in 4 s, then horizontal for 6 s, then falling in a straight line to 0 in the next 2 s. The average speed over the whole 12 s is
Answer: C. 9 m/s
Explanation: Area = 24 + 72 + 12 = 108 m; average speed = 108/12 = 9 m/s.
Q4. A stone is thrown horizontally at 15 m/s from the edge of a 45 m high cliff. Neglecting air resistance, the speed with which it strikes the ground below, to three significant figures, is
Answer: D. 33.5 m/s
Explanation: Fall time = √(2×45/10) = 3 s, so vy = 30 m/s; v = √(15² + 30²) = 33.5 m/s.
Q5. A projectile is launched at angle θ above the horizontal. If its horizontal range equals twice its maximum height, then tan θ equals
Answer: A. 2
Explanation: R = 2u²sinθcosθ/g and H = u²sin²θ/(2g). R = 2H gives 2sinθcosθ = sin²θ, so tan θ = 2.
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Q6. A 4 kg block on a rough horizontal table (μ = 0.2) is joined by a light string over a smooth pulley to a 6 kg block hanging freely. Take g = 10 m/s². The tension in the string while the blocks move is
Q7. A spring balance in a lift shows 4.8 kg for an object whose true mass is 4.0 kg. Take g = 10 m/s². The lift's acceleration, directed upward, is
Q8. The force on a 0.15 kg ball, initially at rest, rises linearly from zero to 600 N and then falls linearly to zero in a total contact time of 0.02 s (triangular F–t graph). The speed of the ball after the contact is
Q9. A 6 kg shell moving at 10 m/s explodes into a 2 kg piece and a 4 kg piece. The 2 kg piece continues forward along the original line at 40 m/s. The speed of the 4 kg piece is
Q10. A 3 kg mass moving with speed u collides and sticks to a 5 kg mass at rest. The fraction of the initial kinetic energy lost in the collision is
Q11. A ball dropped from 5 m rebounds to 3.2 m after its first bounce. Assuming the coefficient of restitution is the same at each bounce, the height reached after the second bounce is
Q12. A 10 kg block is pushed up a rough plane inclined at 37° by a force parallel to the plane so that it moves at constant speed. The coefficient of kinetic friction is 0.5, g = 10 m/s², and sin 37° = 0.6, cos 37° = 0.8. The force needed is
Q13. A 2 kg block rests on a 4 kg block, the coefficient of static friction between them being 0.3. The lower block rests on a frictionless floor and is pulled by a horizontal force F. Take g = 10 m/s². The largest F for which the blocks move together without slipping is
Q14. A boat that can move at 5 m/s in still water crosses a 200 m wide river flowing at 3 m/s. It heads upstream at the angle that makes it travel straight across. The crossing time is
Q15. A stone dropped from the top of a tower covers 35 m in the last second of its fall. Take g = 10 m/s². The height of the tower is
Q16. A rocket of mass 5000 kg ejects exhaust at 2000 m/s relative to itself at a rate of 50 kg/s and rises vertically from rest. Taking g = 10 m/s², its initial acceleration is
Q17. Two bodies of masses 1 kg and 4 kg have equal kinetic energies. The ratio of the momentum of the lighter body to that of the heavier body is
Q18. The position of a particle on a line is x = 5t − t² (x in m, t in s). The total distance it travels in the first 4 s is
Q19. A book rests on a horizontal table. Which of the following is the third-law (action–reaction) pair of the Earth's gravitational pull on the book?
Q20. A 60 kg man stands at one end of a 120 kg boat floating at rest on still water and walks off horizontally so that his speed relative to the boat is 3 m/s. Neglecting water resistance, the speed of the boat relative to the water is
Q21. Sand falls onto a horizontal conveyor belt moving at a constant 2 m/s at a rate of 5 kg/s. The extra horizontal force needed to keep the belt at constant speed is
Q22. A car decelerates uniformly. It passes one point at 30 m/s and a second point 100 m further on at 20 m/s. After the second point it travels a further distance before stopping of
Q23. A 2 kg object moving east at 3 m/s collides with a 1 kg object moving north at 4 m/s and they stick together. The speed of the combined object is
Q24. A projectile is fired at the same speed once at 30° and once at 60° above the horizontal (equal ranges). The ratio of the time of flight at 30° to that at 60° is
Q25. A 2000 kg truck pulls a 1000 kg trailer along a smooth level road with a driving force of 6000 N on the truck. The tension in the coupling between them is
Q26. A 2 kg block is held at rest against a vertical wall by a horizontal push of 50 N. The coefficient of static friction is 0.5 and g = 10 m/s². The friction force acting on the block is
Q27. A 0.2 kg puck slides on ice at 20 m/s toward a smooth straight cushion, its path making 30° with the cushion's surface, and bounces off elastically. The magnitude of the impulse given to the cushion is
Q28. A ball is thrown vertically upward at 25 m/s from the ground (g = 10 m/s²). For how many seconds is it above a height of 20 m?
Q29. A car accelerates uniformly from 10 m/s to 30 m/s while covering 400 m. The time taken is
Q30. A stone is dropped from the top of a 125 m tower at the same instant as a second stone is thrown vertically up from the foot of the tower at 50 m/s. Take g = 10 m/s². The stones meet at a height above the ground of