A car starts moving along a line , first with an acceleration a = 5 m/s² starting from rest , then uniformly and finally decelerating at the same rate comes to rest in total time of 25 seconds (t ¹) ,then average velocity during the time is equal to v= 72 kmph . how long does the particle move uniformly?
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Explanation:
the initial velocityu=0
The time taken and the distance traveled during accelerated motion and retarding motion will be same as the acceleration is same
For accelerated motion
v=u+at=5t
And for retardation
0=v−5t
v=5t
As the velocity v will become u for retardation
Total distance traveled
= area of v−t
= areaI+ area II+ area III
2(
2
1
5t
2
)+5tx=distance traveled during motion
x=time during which particle remains in uniform motion
5t
2
+5tx=speedx time
5t
2
+5tx=20×25
t
2
+tx=100→1
Also the total time is given 25seconds
Thus 2t+x=25
Thus x=25−2t→2
Substituting 2 in 1
t
2
+t(25−2t)=100
t
2
−25t+100=0
t=5 or t=20
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