A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground? After what time will it strike the ground?
Distance covered by the ball, s = 20 m
Acceleration, a = 10 m/s2
Initially, velocity, u = 0
Final velocity, v = ?
Time, t = ?
According to the third equation of motion:
v2 = u2 + 2 as
v2 = 0 + 2 (10) (20)
v = 20 m/s
According to the first equation of motion:
v = u + at
20 = 0 + 10 (t)
t = 2 s
Hence, time taken to reach at the ground is 2 seconds.
Abdul, while driving to school, computes the average speed for his trip to be 20 km h-1. On his return trip along the same route, there is less traffic and the average speed is 40 km h-1. What is the average speed for Abdul’s trip?
A driver of a car travelling at 52 km h-1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h-1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
Fig 8.11 shows the distance-time graph of three objects A,B and C. Study the graph and answer the following questions:
Fig. 8.11
(a) Which of the three is travelling the fastest?
(b) Are all three ever at the same point on the road?
(c) How far has C travelled when B passes A?
(d) How far has B travelled by the time it passes C?
The speed-time graph for a car is shown is Fig. 8.12.
Fig. 8.12
(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
A train starting from a railway station and moving with uniform acceleration attains a speed 40 km h-1 in 10 minutes. Find its acceleration.
A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s-2 for 8.0 s. How far does the boat travel during this time?
During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 108 m s-1.
A train is travelling at a speed of 90 km h-1. Brakes are applied so as to produce a uniform acceleration of – 0.5 m s-2. Find how far the train will go before it is brought to rest.
Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?
A trolley, while going down an inclined plane, has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start?
Which of the following has more inertia: (a) a rubber ball and a stone of the same size? (b) a bicycle and a train? (c) a five-rupees coin and a one-rupee coin?
State the universal law of gravitation.
Which of the following are matter?
Chair, air, love, smell, hate, almonds, thought, cold, cold-drink, smell of perfume.
A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force (Fig. 11.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?
What is meant by a pure substance?
How does the sound produced by a vibrating object in a medium reach your ear?
In a reaction, 5.3 g of sodium carbonate reacted with 6 g of ethanoic acid. The products were 2.2 g of carbon dioxide, 0.9 g water and 8.2 g of sodium observations are in agreement with the law of conservation of mass.
sodium carbonate + ethanoic acid → sodium ethanoate + carbon dioxide + water
What are canal rays?
State any two conditions essential for good health.
How is our atmosphere different from the atmospheres on Venus and Mars?
Fill in the gaps in the following table illustrating differences between prokaryotic and eukaryotic cells.
Prokaryotic Cell | Eukaryotic Cell |
1. Size : generally small (1-10 μm) 1 μm = 10-6 m |
1. Size generally large (5-100 μm) |
2. Nuclear region: ________________ and known as _________________ |
2. Nuclear region: well defined andsurrounded by a nuclear membrane |
3. Chromosome: single |
3. More than one chromosome |
4. Membrane-bound cell organelles absent | 4. _______________________ _______________________ |
List the points of differences between homogeneous and heterogeneous mixtures.
Why is the cell called the structural and functional unit of life?
Name the technique to separate
(i) butter from curd,
(ii) salt from sea-water,
(iii) camphor from salt.
Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
What is the audible range of the average human ear?
If one mole of carbon atoms weighs 12 gram, what is the mass (in gram) of 1 atom of carbon?
An echo returned in 3 s. What is the distance of the reflecting surface from the source, given that the speed of sound is 342 m s-1?
Compare all the proposed models of an atom given in this chapter.
A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.