Tiêu đề 2-kinematics-of-a-particle.pdf ✅

Kinematics of a Particle 1. A spring with one end attached to a mass and the other to a rigid support is stretched and released. (A) Magnitude of acceleration, when just released is maximum (B) Magnitude of acceleration, when at equilibrium position, is maximum (C) Speed is maximum when mass is at equilibrium position (D) Magnitude of displacement is always maximum whenever speed is minimum. 2. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is : (A) 4.0 m/s (B) 5.0 m/s (C) 5.5 m/s (D) 4.8 m/s 3. A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground, (A) The direction of motion of the ball changes every 10 seconds. (B) Speed of ball changes every 10 seconds (C) Average speed of ball over any 20 second interval is fixed (D) The acceleration of ball is the same as from the train 4. The displacement of a particle as a function of time is shown in the figure. The figure shows that (A) The particle starts with certain velocity but the motion is retarded and finally the particle stops (B) The velocity of the particle is constant throughout (C) The acceleration of the particle is constant throughout (D) The particle starts with constant velocity, then motion is accelerated and finally the particle moves with another constant velocity 5. A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u. (A) They meet at time t = u g and at a height u 2 2g + gT 2 8 (B) They meet at time t = u g + T 2 and at a height u 2 2g + gT 2 8 (C) They meet at time t = u g + T 2 and at a height u 2 2g − gT 2 8 (D) They never meet 6. A smooth square platform ABCD is moving towards right with a uniform speed v. At what angle θ must a particle be projected from A with speed u so that it strikes the point B : (A) sin−1 ( u v ) (B) cos−1 ( v u ) (C) cos−1 ( u v ) (D) sin−1 ( v u ) 7. A stone is thrown vertically upward. On its way up it passes point A with speed of v, and point B, 3m higher than A, with speed v/2. The maximum height reached by stone above point B is : (A) 1 m (B) 2m (C) 3 m (D) 5 m 8. A Person can swim in still water at the rate of 3 km/hr. He wants to cross the river so that path traveled by swimmer is minimum. If river is flowing at the rate of 5 km/hr and width of the river is 120 m. Then : (A) Swimmer must swim making angle 127∘ with flow of river (B) Swimmer must swim perpendicular to flow to river (C) Length of possible shortest path is 200 m (D) Length f possible shortest path is 120 m
9. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H, u and n is : (A) 2gH = n 2u 2 (B) gH = (n − 2) 2u 2 (C) 2gH = nu 2 (n − 2) 2 (D) gH = (n − 2) 2u 2 10.Let be the instantaneous velocity and acceleration of a particle moving in a plane. The rate of change of speed dv/dt of the particle is equal to : (A) |a⃗| (B) v⃗⃗⋅a⃗⃗ v (C) The component of a⃗ parallel to v⃗ (D) The component of a⃗ perpendicular to v⃗ 11.Initial acceleration of a particle moving in a straight line is a0 and initial velocity is zero. The acceleration reduces continuity to half in every t0 seconds. The terminal velocity of the particle is : (A) a0t0ln(2) (B) a0t0 ln (2) (C) a0t0 (D) a0t0 2 12.Pick the correct statements : (A) Average speed of a particle in a given time is never less than the magnitude of the average velocity (B) It is possible to have a situation in which | dv ̅ dt | ≠ 0 but d dt |v ̅| = 0 (C) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval (D) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed). 13.Acceleration of a particle which is at rest at x = 0 is a⃗ = (4 − 2x)iˆ. Select the correct alternative(s). (A) Particle further comes to rest at x = 4 (B) Particle oscillates about x = 2 (C) Maximum speed of particle is 4 units (D) All of the above 14.A particle starts from rest and traverses a distance l with uniform acceleration, then moves uniformly over a further distance 2l and finally comes to rest after moving a further distance 3l under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its way is : (A) 1/5 (B) 2/5 (C) 3/5 (D) 4/5 15.The v-s graph for a car in a race on a straight road is given. Identify the correct a − x graph : (a) (b) (c)