A particle starting from rest has a constant acceleration of 4 m/s2 for 4 seconds. It then retards uniformly for next 8 seconds and come to rest. Average speed during the motion of the particle is
Answers
Given :-
◉ A particle starts from rest has a constant acceleration a₁ for time t₁ seconds. It then retards uniformly for t₂ seconds and comes to rest.
To Find :-
◉ Average speed during the motion of the particle
Solution :-
We know that the average speed is the ratio of total distance travelled to total time taken. So we need to find the total distance travelled because total time taken is given as t₁ + t₂
The Journey is divided into two parts:
First :-
The particle starts from rest with a constant acceleration a₁ for time t₁, given that:
- a₁ = 4m/s² , t₁ = 4 s
Since the particle starts from rest, hence its initial velocity u = 0 m/s
Using the second equation of motion, we get
⇒ s₁ = ut + 1/2 at²
⇒ s₁ = 0×4 + 1/2 × 4 × 4²
⇒ s₁ = 2 × 16
⇒ s₁ = 32 m ...(1)
Also, We need to find the final velocity because in the second part we are not given the acceleration, Using first equation of motion:
⇒ v = u + at
⇒ v = 0 + 4×4
⇒ v = 16 m/s ...(2)
Second :-
The final velocity in the first part would now be the initial velocity, u = 16 m/s
We are given in the second part that, the particle comes to rest with a uniform retardation in time t₂ = 8 s
Using first equation of motion,
⇒ v = u + at
⇒ 0 = 16 + 8a [ ∵ particle comes to rest ]
⇒ a₂ = -2 m/s²
Again, Using second equation of motion,
⇒ s = ut + 1/2 at²
⇒ s₂ = 16×8 + 1/2 × -2 × 8²
⇒ s₂ = 128 - 64
⇒ s₂ = 64 m ...(3)
Now,
Total Distance Travelled = s₁ + s₂
⇒ s = 32 + 64
⇒ s = 96 m
Also,
Total Time taken = t₁ + t₂
⇒ t = 4 + 8
⇒ t = 12 s
So,
⇒ Average Speed = s / t
⇒ avg. Speed = 96 / 12
⇒ avg. Speed = 8 m/s
Hence, The average speed of the particle is 8 m/s.
Answer:
avg.speed=8m/s
Explanation:
given : starting from rest u=0
a=4m/s. ,t=4s
solution:
v=u+at
v=0+4*4
v=16m/s
S1=ut+½at²
=0+½*4*4²
=32m
a2=u+at
=16+8a
= -2
S2= ut+½at²
=16*8-½*8²
=64m
total distance=S1+S2
=64+32
=96m
total time=t1+t2
=4+8
=12s
avg.speed=distance/time
=96/12
= 8m/s.
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