ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Motion, Force and Momentum (Set 5): 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 car moving at 20 m s⁻¹ is braked by a driver whose reaction time is 0.5 s; after that the car decelerates uniformly at 5 m s⁻². The total distance travelled from the moment the driver sees the hazard until the car stops is:
Answer: C. 50 m
Explanation: Reaction distance = 20 × 0.5 = 10 m. Braking distance = v²/2a = 400/10 = 40 m. Total = 50 m.
Q2. A police car starts from rest with acceleration 4 m s⁻² just as a speeding car passes it at a constant 20 m s⁻². The police car's speed when it catches the speeder is:
Answer: C. 40 m s⁻¹
Explanation: Equal displacements: ½(4)t² = 20t gives t = 10 s. Police speed = 4 × 10 = 40 m/s (twice the speeder's speed).
Q3. A train's velocity rises uniformly from 0 to 10 m s⁻¹ in 5 s, stays at 10 m s⁻¹ for 10 s, then falls uniformly to zero in 5 s. Its average speed over the whole 20 s is:
Answer: B. 7.5 m s⁻¹
Explanation: Area under the v–t graph = ½(5)(10) + 10×10 + ½(5)(10) = 25 + 100 + 25 = 150 m. Average speed = 150/20 = 7.5 m/s.
Q4. A ball is thrown vertically upward at 30 m s⁻¹ (g = 10 m s⁻²). It passes the height of 25 m twice. The time between these two passes is:
Answer: A. 4 s
Explanation: 25 = 30t − 5t² → t² − 6t + 5 = 0 → t = 1 s and 5 s. Interval = 4 s.
Q5. A stone is dropped from a tower and covers 45 m during its last second of fall (g = 10 m s⁻²). The height of the tower is:
Answer: D. 125 m
Explanation: Distance in the last second = g(T − ½) = 45 → T = 5 s. Height = ½(10)(25) = 125 m.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. A ball is kicked horizontally at 30 m s⁻¹ from the edge of a cliff 80 m high (g = 10 m s⁻², air resistance ignored). Its speed just before hitting the ground is:
Q7. A projectile is fired at 50 m s⁻¹ at 53° above the horizontal (take sin53° = 0.8, cos53° = 0.6, g = 10 m s⁻²). After 2 s, the direction of its velocity relative to the horizontal is closest to:
Q8. A stone is thrown at 20 m s⁻¹ from the ground at some unspecified angle (g = 10 m s⁻²). Its speed when it is 10 m above the ground is:
Q9. Two projectiles are launched with the same speed, one at 30° and the other at 60° to the horizontal. The ratio of their maximum heights (30° : 60°) is:
Q10. A 60 kg man stands in a lift that is moving upward but slowing down at 2 m s⁻² (g = 10 m s⁻²). The reading of a weighing scale under his feet is:
Q11. A 5 kg block on a table with μ = 0.2 is joined by a light string over a smooth pulley at the table edge to a 3 kg mass hanging freely (g = 10 m s⁻²). The acceleration of the system is:
Q12. Three blocks of 2 kg, 3 kg and 5 kg are in contact in a row on a smooth horizontal floor, with a 20 N horizontal force pushing on the 2 kg block. The force exerted by the 3 kg block on the 5 kg block is:
Q13. A block slides from rest down a rough 37° incline (sin37° = 0.6, cos37° = 0.8, μ_k = 0.25, g = 10 m s⁻²). The time taken to slide 8 m along the incline is:
Q14. A book rests on a horizontal table. The Earth pulls the book downward with its weight. According to Newton's third law, the reaction to this force is:
Q15. A 20 g bullet embeds itself in a 1.98 kg block suspended by a long string. The block with the bullet rises vertically 0.2 m (g = 10 m s⁻²). The speed of the bullet before impact was:
Q16. A 60 kg man stands at one end of a 40 kg boat that is at rest on still water. He walks 5 m toward the other end, relative to the boat. Ignoring water resistance, the boat moves by:
Q17. A 3 kg object moving east at 2 m s⁻¹ collides with and sticks to a 2 kg object moving north at 4 m s⁻¹. The speed of the combined object is:
Q18. A 3 kg cart moving at 4 m s⁻¹ strikes a stationary 1 kg cart in a perfectly elastic head-on collision on a frictionless track. The speed of the 1 kg cart afterwards is:
Q19. A ball dropped from 1.8 m above a hard floor bounces back to a height of 0.8 m. The coefficient of restitution is:
Q20. A force acting on a 2 kg body at rest rises linearly from zero to 40 N in 0.5 s and then drops to zero instantaneously. The final speed of the body is:
Q21. A 0.5 kg ball strikes a smooth wall at 10 m s⁻¹, with its velocity making 60° with the normal to the wall, and rebounds elastically. The magnitude of the impulse given to the ball is:
Q22. A rocket of mass 500 kg (including fuel) burns fuel at 5 kg s⁻¹ and ejects gas at 2000 m s⁻¹ relative to itself. At launch from rest its upward acceleration is (g = 10 m s⁻²):
Q23. Two bodies have the same momentum, but their masses are in the ratio 1 : 4. The ratio of their kinetic energies (lighter : heavier) is:
Q24. A 50 kg person jumps from a platform 1.8 m high, landing on firm ground and stopping in 0.2 s (g = 10 m s⁻²). The average force exerted by the ground on the person during the stop is:
Q25. Rain falls vertically at 8 m s⁻¹. A cyclist riding on a level road at 6 m s⁻¹ holds an umbrella to keep dry. The umbrella's axis should make an angle with the vertical of:
Q26. A swimmer who can swim at 5 m s⁻¹ in still water heads directly across a 100 m wide river flowing at 3 m s⁻¹. The distance the swimmer is carried downstream is:
Q27. An athlete runs 1.5 laps on a circular track of circumference 400 m, starting at a point A. The distance travelled and the magnitude of displacement from A are:
Q28. A cyclist rides three equal stretches of a road at 20 km h⁻¹, 30 km h⁻¹ and 60 km h⁻¹ respectively. The average speed for the whole ride is:
Q29. A box rests on the flat bed of a truck. The coefficient of static friction between the box and bed is 0.4 (g = 10 m s⁻²). The maximum acceleration the truck can have without the box slipping is:
Q30. Sand falls vertically at a steady 2 kg s⁻¹ onto a horizontal conveyor belt that moves at a constant 3 m s⁻¹. The extra horizontal force needed to keep the belt moving at constant speed is: