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Question
Suggest a suitable physical situation for the following graphs:
Solution
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A particle moves along the X-axis as x = u (t − 2 s) + a (t − 2 s)2.
(a) the initial velocity of the particle is u
(b) the acceleration of the particle is a
(c) the acceleration of the particle is 2a
(d) at t = 2 s particle is at the origin.
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A particle starts from the origin, goes along the X-axis to the point (20 m, 0) and then return along the same line to the point (−20 m, 0). Find the distance and displacement of the particle during the trip.
In the following figure Shows the graph of velocity versus time for a particle going along the X-axis. Find the displacement in 0 to 10 s.
Refer to the graphs in figure. Match the following.
| Graph | Characteristic |
(a)  |
(i) has v > 0 and a < 0 throughout. |
(b)  |
(ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0. |
(c)  |
(iii) has a point with zero displacement for t > 0. |
(d)  |
(iv) has v < 0 and a > 0. |
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- Plot qualitatively velocity vs time graph.
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A man runs across the roof-top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is of a lower height than the first. If his speed is 9 m/s, the (horizontal) distance between the two buildings is 10 m and the height difference is 9 m, will he be able to land on the next building? (take g = 10 m/s2)
The velocity-displacement graph of a particle is shown in figure.
- Write the relation between v and x.
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Ship A is sailing towards the northeast with velocity `vecv = 30hati + 50hatj` km/hr where `hati` points east and `hatj`, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing west at 10 km/hr. A will be at the minimum distance from B in ______.
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