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Question

A car starting from rest accelerates at the rate f through a distance s, then continues at constant speed for time t and then decelerates at rate f2 to come to rest. If the total distance covered is 15s, then which one is correct?

A
s=ft272
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B
s=ft24
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C
s=ft26
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D
s=ft22
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Solution

The correct option is A s=ft272
When the car starts from rest and accelerates at the rate f
Distance covered is given by,
s=0+12ft21(1)
t1=2sf
Velocity of the car after time t1 is
v=0+ft1
v=ft1
Distance covered with constant speed v in time t is given by
s=vt=(ft1)t(2)
Velocity of the car after time t2 is 0 and let the distance covered be s′′
v2=u2+2ax
0=v22(f2)s′′v2=fs′′
s′′=(v2f)=f2t21f=ft21(3)
We know that s+s+s′′=15s
s+s′′=14s
Using (1), (2) and (3) we get
(ft1)t+ft21=14 s
(ft1)t+2s=14s(ft)t1=12s
s=(ft12)t1=(ft12)2sfs2=f2t2144×2sfs=(ft272)

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