Title 3. Motion in a Straight Line.pdf ✅

1. A particle moves along a straight line such that its displacement at any time t is given by : The displacement when the acceleration becomes zero is : (1)0 m (2) 2 m (3) 3 m (4) –2 m 2. The displacement x of a particle varies with time t as x = ae–t + bet , where a, b,  and  are positive constants. The velocity of the particle will:- (1) be independent of  (2) drop to zero when  =  (3) go on decreasing with time (4) go on increasing with time 3. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by :- x = 40 + 12t – t 3 How long would the particle travel before coming to rest? (1) 16 m (2) 24 m (3) 40 m (4) 56 m 4. A particle is projected vertically upwards from a point A on t he ground. It takes time t1to reach a point B, but it still continues to move up. If it takes further t2time to reach the ground from point B. Then height of point B from the ground is– 5 . A particle is released from rest from a tower of height 3 h. The ratio of times to fall equal heights h, i.e. , t1 : t2 : t3 is– 1) 3 : 2 :1 2) 3: 2:1 3) 9: 4:1 4) 1: 2 1 : 3 2 ( − − ) ( ) 6 . A particle is moving along x-axis and graph between square of speed and position of the particle is given in the figure if at t = 0, x = 0 m, select incorrect statement – (1) Acceleration of the particle is 15 m/s2 at 1 2 t s = (2) Acceleration of the particle is 7.5 m/s2 at t= 1 s (3) Acceleration of the particle is constant (4) At t = 1 s, velocity of particle is 12.5 m/s 7. An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 ms–2 . 2 sec after the start, a bolt begins fallings from the ceiling of the car. The free fall time of the bolt is :- (1) 0.54 s (2) 6 s (3) 0.7 s (4) 1 s A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion. B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion. C. If Assertion is True but the Reason is False. D. If both Assertion & Reason are False. 8. Assertion :- The position-time graph of a uniform motion in one dimension of a body can have negative slope. Reason :- When the speed of body decreases with time, the position-time graph of the moving body has negative slope. (1) A (2) B (3) C (4) D 9. At time t = 0s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time 't', the net force acting on it must be proportional to :- Motion in a Straight Line
(1) t (2) constant (3) t (4) 1 t 10. Speeds of two identical cars are u and 4u at a specific instant. The ratio of the respective distances at which the two cars are stopped from that instant is- (1) 1 : 1 (2) 1 : 4 (3) 1 : 8 (4) 1 : 16 11. 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 : (1) 2g H = nu2 (n – 2) (2) g H = (n – 2)u2 (3) 2g H = n2u 2 (4) g H = (n – 2)2u 2 12. A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 S, then- 13. When a train is at rest, rain drops fall vertically. When it moves along east with a velocity equal to that of rain, the rain will appear to fall, for a passenger in the train (1) Along north-east (2) Along north-west (3) From upwards (4) 45° to vertical 14. A body is dropped from the top of a tower of height h metres. It takes T seconds to reach the ground. After T/2 seconds it will be at a height: (1) h/2 metres from the ground (2) h/4 metres from the ground (3) 3h/4 metres from the ground (4) Cannot be answered from the data 15. A particle moves in a straight line so that its displacement x in metres at time t seconds is given by 2 t x = −1 . Its acceleration in ms–2 at t seconds is :- 16. An object is moving with a speed of 6.25 m/s and is decelerated at a rate given by 1/2 2.5 dv v dt = − where v is the instantaneous speed. The time taken by the object to come to rest would be. (1) 4 s (2) 8 s (3) 1 s (4) 2 s 17. The velocity V of a moving particle varies with displacement as x = V +1 , the acceleration of the particle at x = 5 unit will be :- (1) 6 unit (2) 24 unit (3) 240 unit (4) 25 unit 18. The displacement-time graph of a particle moving on the x -axis is given below :- then : (1) The particle is continuously going in +x-direction (2) The particle is at rest (3) The velocity increases up to a time 't0' and then become constant (4) The particle moves at a constant velocity up to a time 't0' and then stops. 19. A ball is dropped from a height. If it takes 1sec to cross the last 55m before hitting the ground find the height from which it was dropped :- (1) 55 m (2) 50 m (3) 90 m (4) 180 m 20. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be :-
21. Figure shows velocity-time graph of a particle which moves along a straight line. Then choose incorrect statement (1) Distance travelled by particle is 212.5 m (2) Distance covered by particle with constant velocity is 100 m (3) Velocity of particle at t = 25 sec is 5 m/s (4) Velocity of particle at t = 15 sec is 10 m/s 22. A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is :- 23. The velocity v of a particle is given by the equation v = 6t 2 – 6t 3 , where v is in m/sec and t is time in seconds then :- (1) at t = 0, velocity is maximum (2) at t = 2 3 , velocity is minimum (3) minimum velocity is zero (4) minimum velocity is –2 m/sec 24. A particle moves with uniform acceleration andv1, v2 and v3 denote the average velocities in the three successive intervals of time t1, t2 and t3.Which of the relations given below is correct? (1) (v1 – v2) : (v2 – v3) = (t1 – t2) : (t2 + t3) (2) (v1 – v2) : (v2 – v3) = (t1 + t2) : (t2 + t3) (3) (v1 – v2) : (v2 – v3) = (t1 – t2) : (t1 – t3) (4) (v1 – v2) : (v2 – v3) = (t1 – t2) : (t2 – t3) 25. A body is thrown vertically upwards from the top A of a tower. It reaches the ground in t1seconds.If it is thrown vertically downwards from the same tower with the same speed it reaches the ground in t2 seconds. If it is allowed to fall freely from the same tower, then the time it takes to reach the ground is given by :- (1) 1 2 2 t t t + = (2) 1 2 2 t t t − = (3) 1 2 t t t = (4) 1 2 t t t = 26. A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the nth second to that covered in n seconds is :- (1) 2 2 1 n n − (2) 2 2 1 n n + (3) 2 2 1 n n − (4) 2 2 1 n n + 27. A train 200 m long crosses a bridge 300 m long. It enters the bridge with a speed of 30ms–1 and leaves it with a speed of 50 ms–1 . What is the time taken to cross the bridge ? (1) 2.5 s (2) 7.5 s (3) 12.5 s (4) 15.0 s 28. A body is released from the top of a tower of height H metre. After 2 seconds it is stopped and then instantaneously released. What will be its height after next 2 seconds :- (1) (H – 5) metre (2) (H – 10) metre (3) (H – 20) metre (4) (H – 40) metre
29. If a particle moves along a straight line according to the law v=2 (x sinx + cos x) then find its acceleration (i.e. dv dt ) at x=  /2 (1) 2  (2) 2 2  (3) 4 2  (4) zero 30. While sitting on a tree branch 20m above the ground, you drop a chestnut. When the chestnut has fallen 5m, you throws a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time? (g=10ms–2 ) (1) 5 ms–1 (2) 10 ms–1 (3) 15 ms–1 (4) None of these 31. A particle is moving in a straight line y=3x. Its velocity time graph is shown in figure. Its speed is minimum at t =............. (1) 2s (2) 4s (3) 6s (4) 8s 32. A ball is thrown vertically upwards from the top of a tower at 4.9 ms–1 . It strikes the pond near the base of the tower after 3 seconds. The height of the tower is :- (1) 73.5 m (2) 44.1 m (3) 29.4 m (4) None of these 33. A body starts from rest is moving under a constant acceleration up to 20 sec. If it moves S1 distance in first 10 sec., and S2 distance in next 10 sec. then S2will be equal to : (1) S1 (2) 2S1 (3) 3S1 (4) 4S1 34. Two bodies, A (of mass 1 kg) and B (of mass 3kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by the m to reach the ground is :- (1) 5 4 (2) 12 5 (3) 5 12 (4) 4 5 35. A particle moves a distance x in time t according to equation x = (t+5)–1 . The acceleration of particle is proportional to :- (1) (velocity)2/3 (2) (velocity)3/2 (3) (distance)2 (4) (distance)–2 36. A particle of unit mass undergoes one dimensional motion such that its velocity varies according to ( ) 2n v x x  − = where  and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by : (1) 2 4 1 2 n n x  − − − (2) 2 2 1 2 n  x − + − (3) 2 4 1 2 n n e  − + − (4) 2 2 1 2 n n x  − − − 37. A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one half of its maximum height. How high does the ball rise?(Take g = 10 m/s2 ). (1) 5m (2) 15m (3) 10 m (4) 20 m 38. The velocity-time graph of a car moving along a straight road is shown in figure.