Questions and Answers
What is the distance covered by a particle in the fifth second of its motion if it has an initial velocity of 9 m/s due east and a constant acceleration of 2 m/s² due west?
How high is the tower from which a stone is dropped, given another stone is dropped 20 m below the top and both stones reach the bottom simultaneously?
What is the average speed of a train that accelerates uniformly from rest, then moves at a constant velocity, and finally retards uniformly, with a maximum speed of 60 km/h?
If a particle is thrown upwards and experiences a constant retardation of 2 m/s², what is the ratio of time of ascent to time of descent when g is 10 m/s²?
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What is the formula for the distance covered in t seconds by a point moving under the retardation av², with an initial velocity u?
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What should be the ratio of the vertical velocity v2 of a body projected upwards from point B to the horizontal velocity v1 of a body projected from point A for both to collide?
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A body is projected from a certain height. How does the initial velocity u and the retardation affect the distance covered in t seconds?
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If a train travels 120 km in total with varying speed due to acceleration and deceleration, what might be its average speed if time ratios are 1:8:1?
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Study Notes
Distance Covered by a Particle
- A particle with an initial velocity of 9 m/s east, experiences a constant acceleration of 2 m/s² west.
- To determine the distance covered in the fifth second, consider motion equations which can give insights into distances at specific intervals.
Dropped Stone Problem
- A stone is dropped from a tower height ( h ).
- After 1 second, another stone is dropped from a balcony 20 m below the top.
- Both stones reach the ground simultaneously with gravity ( g = 10 ) m/s².
- Calculate height ( h ) using kinematic equations to find when both stones land.
Train Motion Dynamics
- A train accelerates from rest, maintains a constant speed, and then decelerates to stop.
- The time ratio for these phases is 1:8:1.
- The maximum speed of the train is 60 km/h.
- Use the formula for average speed over variable motion to find the average speed for the entire journey.
Retardation Motion Equation
- A particle moves in a straight line with retardation proportional to the square of its velocity, ( a v^2 ).
- To derive the distance covered in ( t ) seconds, apply calculus to integrate under the retarding force terms.
Ascent and Descent Time Ratio
- A particle is projected upwards experiencing a constant retardation of 2 m/s² due to resistance.
- The ratio of time taken to ascend vs. descend is influenced by gravitational acceleration ( g = 10 ) m/s².
- Apply kinematic principles to relate ascent and descent phases to determine their ratio.
Collision of Projected Bodies
- Two bodies are projected: one from point A horizontally, the other straight up from point B.
- Point B is vertically beneath the apex of the first body’s trajectory.
- For a successful collision, derive the ratio ( v2/v1 ) so that the time of flight aligns for both bodies under gravitational influence.
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Description
Test your understanding of dynamics in physics with this quiz focused on particle motion and acceleration. Solve problems involving velocity, distance, and free-fall scenarios. Perfect for students studying mechanics at various levels.
