NEET 2007
Exam NEET
Year 2007
Subject Physics
Chapter Motion in One Dimension NEET 2007 · Physics · Motion in One Dimension
A particle moving along x -axis has acceleration f , at time t ,...
A particle moving along
x x x -axis has acceleration
f f f , at time
t t t , given by
f = f= f = f 0 ( 1 − t T ) f_0\left(1-\frac{t}{T}\right) f 0 ( 1 − T t ) , where
f 0 a n d f_0 and f 0 an d T
a r e c o n s t a n t s . T h e p a r t i c l e a t are constants.
The particle at a reco n s t an t s . T h e p a r t i c l e a t t=0
h a s z e r o v e l o c i t y . I n t h e t i m e i n t e r v a l b e t w e e n has zero velocity. In the time interval between ha szero v e l oc i t y . I n t h e t im e in t er v a l b e tw ee n t=0
a n d t h e i n s t a n t w h e n and the instant when an d t h e in s t an tw h e n f=0
, t h e p a r t i c l e ′ s v e l o c i t y ( v x ) , the particle's velocity \left(v_x\right) , t h e p a r t i c l e ′ s v e l oc i t y ( v x ) is:
Options A 1 2 f 0 T 2 \frac{1}{2} f_0 T^2 2 1 f 0 T 2 B f 0 T 2 f_0 T^2 f 0 T 2 C 1 2 f 0 T \frac{1}{2} f_0 T 2 1 f 0 T D f 0 T f_0 T f 0 T Correct answer C. 1 2 f 0 T \frac{1}{2} f_0 T 2 1 f 0 T
Step-by-step solution
Acceleration
d v d t = f = f 0 ( 1 − t T ) \frac{d v}{d t}=f=f_0\left(1-\frac{t}{T}\right) d t d v = f = f 0 ( 1 − T t ) ⇒ 0 v d v = f 0 T 1 − t T d t ⇒ v = f 0 ( t − t 2 2 T ) 0 T v = f 0 ( T − T 2 2 T ) = 1 2 f 0 T \begin{aligned}
\Rightarrow{ }_0^v d v & =f_0^T 1-\frac{t}{T} d t \\
\Rightarrow \quad v & =f_0\left(t-\frac{t^2}{2 T}\right)_0^T \\
& v =f_0\left(T-\frac{T^2}{2 T}\right)=\frac{1}{2} f_0 T
\end{aligned} ⇒ 0 v d v ⇒ v = f 0 T 1 − T t d t = f 0 ( t − 2 T t 2 ) 0 T v = f 0 ( T − 2 T T 2 ) = 2 1 f 0 T $$
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