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A particle starts from rest and moves with a constant acceleration of A1 metre per second square air and then decelerates to come rest at constant acceleration of A2 metre per second square if the time for which particle is in motion is T1 then the total distance travelled by the particle is?
Most Upvoted Answer
A particle starts from rest and moves with a constant acceleration of ...
Solution:

Given:
Initial velocity (u) = 0
First acceleration (a1) = A1
Second acceleration (a2) = -A2 (deceleration)
Time for which particle is in motion (t) = T1

Formula:
Distance = ut + (1/2)at^2 (when acceleration is constant)
Distance = (1/2)(u+v)t (when acceleration is not constant)

Calculation:
Phase 1: Constant acceleration (A1)
Distance covered in time T1/2 = (1/2)*A1*(T1/2)^2 = (1/8)*A1*T1^2
Velocity after T1/2 time = u + A1*(T1/2) = (1/2)*A1*T1

Phase 2: Deceleration (-A2)
Let the time taken to come to rest be T2
Final velocity = u + a*t = 0
=> -A2*T2 = -(1/2)*A1*T1
=> T2 = (1/2)*(A1/A2)*T1
The distance covered in time T2 = (1/2)*(-A2)*(T2)^2 = (1/8)*(A1/A2)^2*T1^2

The total distance travelled by the particle is the sum of distances covered in phase 1 and phase 2.
Total distance = (1/8)*A1*T1^2 + (1/8)*(A1/A2)^2*T1^2
= (1/8)*T1^2*(A1 + A1^2/A2^2)

Therefore, the total distance covered by the particle is (1/8)*T1^2*(A1 + A1^2/A2^2).
Community Answer
A particle starts from rest and moves with a constant acceleration of ...
Total distance = V^2+u^2/2(A1+A2)m .....(In first case the distance is x=v^2/2A1,,In second case the distance is u^2/2A2 due to constant acceleration ).(And T1=0). I hope it help !!....
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A particle starts from rest and moves with a constant acceleration of A1 metre per second square air and then decelerates to come rest at constant acceleration of A2 metre per second square if the time for which particle is in motion is T1 then the total distance travelled by the particle is?
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A particle starts from rest and moves with a constant acceleration of A1 metre per second square air and then decelerates to come rest at constant acceleration of A2 metre per second square if the time for which particle is in motion is T1 then the total distance travelled by the particle is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle starts from rest and moves with a constant acceleration of A1 metre per second square air and then decelerates to come rest at constant acceleration of A2 metre per second square if the time for which particle is in motion is T1 then the total distance travelled by the particle is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from rest and moves with a constant acceleration of A1 metre per second square air and then decelerates to come rest at constant acceleration of A2 metre per second square if the time for which particle is in motion is T1 then the total distance travelled by the particle is?.
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