General
✓✗The displacement x of a particle varies with time t as \( x = ae^{-\alpha t} + be^{\beta t} \), where a, b, α and β are positive constants. The velocity of the particle will
- be independent of β
- drop to zero when α = β
- go on increasing with time
- go on decreasing with time
General
✓✗The stopping distance of a car moving at speed v is d. If the same braking force acts, the stopping distance at speed 3v is
- \( \sqrt{3}d \)
- 6d
- 3d
- 9d
General
✓✗A ball is thrown vertically up and returns to the thrower’s hand after rising 5 m. The total distance and the displacement are
- 10 m, 10 m
- 0, 10 m
- 10 m, 0
- 5 m, 5 m
General
✓✗A car starts from rest and accelerates uniformly. It covers 50 m between the 4th and 6th second, i.e. from t = 4 s to t = 6 s. Its acceleration is
- 2.5 m s−2
- 5 m s−2
- 10 m s−2
- 4 m s−2
General
✓✗The position of a particle is \( x = 5t^2 \) (x in m, t in s). Its velocity at t = 2 s is
- 5 m/s
- 40 m/s
- 20 m/s
- 10 m/s
General
✓✗The position of a particle is \( x = t^3 - 12t + 3 \). The particle is momentarily at rest at
- t = 2 s
- t = 3 s
- t = 1 s
- t = 4 s
General
✓✗In the absence of air resistance, a heavy stone and a light feather dropped from the same height reach the ground
- with the feather first
- with the stone first
- together
- depending on their shapes
General
✓✗Assertion: The distance travelled by a body in a given time interval can never be less than the magnitude of its displacement.
Reason: Displacement is the shortest distance between the initial and final positions.
Reason: Displacement is the shortest distance between the initial and final positions.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗A particle moves half the time with speed v1. For the remaining half time, it moves with speed v2 for half of that time and v3 for the other half. Its average speed is
- \( \dfrac{v_1 + 2v_2 + 2v_3}{5} \)
- \( \dfrac{v_1 + v_2 + v_3}{3} \)
- \( \dfrac{2v_1v_2v_3}{v_1+v_2+v_3} \)
- \( \dfrac{2v_1 + v_2 + v_3}{4} \)
General
✓✗A car A moving at 54 km/h overtakes car B moving at 36 km/h in the same direction. The speed of A relative to B in m/s is
- 15 m/s
- 25 m/s
- 5 m/s
- 18 m/s
General
✓✗A train of length 150 m is going towards the north at a speed of 10 m/s. A parrot flies at 5 m/s towards the south, parallel to the railway track. The time taken by the parrot to cross the train is
- 8 s
- 12 s
- 10 s
- 15 s
General
✓✗Two balls are thrown simultaneously, A vertically upwards with 20 m/s and B vertically downwards with 20 m/s, from the same point high above the ground. Their separation after 2 s is
- 80 m
- 20 m
- 0
- 40 m
General
✓✗Two cars start from rest at the same point with uniform accelerations of 2 m s−2 and 3 m s−2 along the same straight road. Their separation after 10 s is
- 100 m
- 25 m
- 50 m
- 500 m
General
✓✗The position of a particle varies as \( x = 6t - t^2 \) (x in m, t in s). The distance travelled by the particle in the first 4 s is
- 8 m
- 16 m
- 9 m
- 10 m
General
✓✗Two trains move towards each other on parallel tracks with speeds of 50 km/h and 70 km/h. The speed of one with respect to the other is
- 20 km/h
- 120 km/h
- 35 km/h
- 60 km/h