MOTION IN ONE DIMENSION
1. Give example where
a) The velocity is in opposite direction to the acceleration
b) The velocity of the particle is zero but acceleration is not zero
c) The velocity of perpendicular to the acceleration
2. A particle is moving in the circle of radius 4 cm with constant speed of 1 cm/s. Find
a) Time period of the particle
b) Average speed, average velocity and average acceleration in a time interval from t=0 to t=T/4. Here, T is the time period of the particle.
3. A particle moving in a straight line with constant speed of 4 m/s for 2 s, then with 6 m/s for 3 s. Find the average speed of the particle in the given interval of time.
4. A ball is thrown upward from the top of a tower 40 m high with a velocity of 10 m/s. Find the time when it strikes the ground.
5. A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80 m at two times, the time interval being 6 s. Find u.
6. A particle is projected vertically upwards with velocity 40 m/s. Find the displacement and distance travelled by the particle in
a) 2 s b) 4 s c) 6 s
7. Displacement-time equation of a particle moving along x-axis is x=20 + t3 -12t
a) Find, position and velocity of particle at time t=0.
b) State whether the motion is uniformly accelerated or not.
c) Find position of the particle when the velocity of the particle is zero.
8. Seeta is moving due east with a velocity of 1 m/s and geeta is moving due west with a velocity of 2 m/s. What is the velocity of seeta with respect to geeta.
9. Car A has an acceleration of 2 m/s2 due east and car B has an acceleration of 43 m/s2 due north. What is the acceleration of car B with respect to car A?
10. Car A and car B start moving simultaneously in the same direction along the line joining them. Car A with a constant acceleration 4 m/s2, while car B moves with a constant velocity v=1 m/s. AT time t=0, car A is 10 m behind the car B. Find the time when car A overtakes car B.
11. An open lift is moving upwards with velocity 10 m/s. It has an upward acceleration of 2 m/s2. A ball is projected upwards with velocity 20 m/s relative to ground. Find:
a) Time when ball again meet the lift.
b) Displacement of lift and ball at that instant.
c) Distance travelled by the ball upto that instant.
12. A river 400 m wide is flowing at the rate of 2 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water in the direction perpendicular to the river.
a) Find the time taken by the boat to reach the opposite bank.
b) How far from the point directly opposite to the starting point does the boat reach the opposite bank.
13. Two particles A and B start moving simultaneously along the line joining them in the same direction with the acceleration of 1 m/s2 and 2 m/s2 and speeds 3 m/s and 1 m/s respectively. Initially A is 10 m behind B. What is the minimum distance between them?
14. To a man walking at a rate of the 3 km/h the rain appears to fall vertically. When he increases his speed to 6 km/h it appears to meet with the angle of 45˚ with vertical. Find the speed of rain.
15. A stone is dropped from the top of the tower. When it crosses a point 5m below the top, another stone is let fall from a point 25 m below the top. Both stones reaches the bottom of the tower simultaneously. Find the height of the tower.
16. A football is kicked vertically upwards from the ground and a student gazing out of the window sees it moving upwards past her at 5 m/s. The window is 15 m above the ground. Air resistance may be neglected. Take g=10 m/s2.
a) How high does the football go above the ground?
b) How much time does it take to go from the ground to its highest point?
17. X-coordinates of the particles moving along this axis is x = (2+t2+2t3). Here, x is in the meter and t is in second. Find
a) Position of the particle from where it started its journey.
b) Initial velocity of particle and
c) Acceleration of the particle at t = 2s.
18. The velocity of the particle moving in a straight line is decreasing at the rate of 2 m/s per meter of the displacement at an instant when the velocity is 10 m/s. Determine the acceleration of the particles at that instant.
19. The position of the particle along the straight line is given by s = (t3-9t2-15t) m, here t is in seconds. Determine the maximum acceleration during the time interval 0 ≤ t ≤ 10 sec.
20. A ball is thrown vertically upwards from the 12 m level with an initial velocity of 18 m/s. At the same time an open platform elevator passes the 5 m level, moving upwards with a constant velocity of 2 m/s. Determine(g = 9.8 m/s2)
a) When and where the ball will meet the elevator,
b) The relative velocity of the ball with respect to the elevator when the ball hits the elevator.
21. An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.2 m/s2 and the automobile has an acceleration of 3.5 m/s2. The automobile overtakes the truck when it (truck) has moved 60 m.
a) How much time does it takes the automobile to overtakes the truck?
b) How far was the automobile behind the truck initially?
c) What is the speed of each during overtaking?
22. A body is thrown up in the lift with a velocity u relative to the lift and the time of flight is t. Show that the lift is moving up with an acceleration (2u-tg)/t.
23. A river is 20 m wide. River speed is 3 m/s. A boat starts with velocity 2√2 m/s at angle 45˚ from the river current (relative to river)
a) Find the time taken by the boat to reach the opposite bank.
b) How far from the point directly opposite to the starting point does the boat reach the opposite bank?
24. An aeroplane has to go from a point P to another point Q, 1000 km away due north. Wind is blowing due east at a speed of 200 km/h. The air speed of plane is 500 km/h.
a) Find the direction in which the pilot should head the plane to reach the point Q.
b) Find the time taken by the plane to go from P to Q.
CLICK HERE FOR INTERESTING FACTS
No comments:
Post a Comment