GENERAL APPTITUDE FOR CSIR NET
MOTION
Notions :
we denote physical quantities by a special and unique symbol to avoid confusion.
time t ;
speed v ; and veocity v;
acceleration a;
initial velocity u;
final velocit v ;
average speed w ;
average velocity w ;
radius of circle r;
angular displacement θ ;
angular velocity ω ;
IMPORTANT FORMULA :
Distance travelled = speed × time or s = v × tDisplacement = velocity × time or s = v × t
Average speed = ( total distance travelled ) ÷ ( total time taken)
Average velocity = ( initial velocity + final velocity ) ÷ 2 or w = (u + v) ÷ 2
Acceleration = ( Change in velocity ) ÷ ( time taken ) or
= ( final velocity - initial velocity ) ÷ time taken or a = ( v – u ) ÷ 2
Linear velocity = angular velocity × radius of the circle.
Equations of Motion : 1) v = u + at
2) s = ut + 1/2 at²
3) v² = u² + 2as
Now solving some problems based on motions
Q 1) A car traveles 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.
Q 2) Rahim driving his motorbicycle and go to office. He computes the average speed for the trip to be 20 km/h . on the return trip along the same route, there is less traffic and the average speed is 40 km/h. What is the average speed for Rahim’s total trip?
Q 3) On a 120 km track, the train travels first 30 km at uniform sped of 30 km/h. How fast must the train travel the next 90 km so as to average speed 60 km/h for the entire trip ?
Q 4) A ball hits a wall horizontally at 6.0 m/s. It rebounds horizontally at 4.4 m/s. The ball is in contact with the wall for 0.040 s. What is the acceleration of the ball ?
Q 5) A car travels 100 km at aspeed of 60 km/h and return with speed of 40 km/h. Calculate the average speed for the whole journey.
Q 6) A ball is thrown vertically upwardswith an initial velocity of 50 m/s. After 1 sec, another ball is thrown upwards with the same initial velocity and in the same line. When and where will the two balls meet ?
Q 7) two trains each having a speed of 30 km/h are headed at each other on the same straight track. A bird that can fly 60 km/h flies off one train when they are 60 km apart and heads directly for the other train. On reaching the other train, it flies back to the first train and so forth.
(a) How many trips can the bird make from one train to the other before they crash ?
(b) What is the total distance the bird travels ?
Q 8) A police car is chasing a car of a theif. The velocity of police car is 30 km/h and that of theif’s car is 192 km/h. A bullet is shot from the police car with a speed of 150 m/s. With what velocity does the bullet hits the theif’s car ?
Q 9) The radius of circular park is 1 km. A cyclist start from the centre O, reaches the point P on the circumference, travels along the circumference to Q and finally returns to the centre O along QO. If the entire journey takes 10 minutes. Calculate the following :
(a) Net displacement
(b) Average velocity
(c) Average speed of the cyclist
Q 10) An aeroplane is flyimg with a speed of 500 km/h. The velocity of the exhaust gases reltive to the plane is 1500 km/h. Find the velocity of the exhaust gases relative to an observer on the ground.
Q 11) the rain drops are falling vertically with a velocity of 30 m/s. A man is cycling from north to south with a velocity of 10 m/s. In which direction he should keek his umbrella ?
Answers
- 26.6 km/h
- 26.7 km/h
- 90 km/h
- -260 m/s
- 48 km/h
- Time = 5.5 second and distance 123.75 m
- (a) the bird completes infinite number of trip from one train to other before they crash
8. 105 m/s
9. (a) 0
(b) 0
(c) 21.42 km/h
10. -1000 Km/h
11. tan¥ = 0.3333
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