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Standard XII

Physics

Relating Circular Motion to SHM

Q.2. A partic...

Question

Q.2. A particle moving in a straight line inital velocity u and uniform acceleration f. If the sum of the distance travelled in $t^{t h}$ and ${(t + 1)}^{t h}$ second is 100 cm, then its velocity after t seconds in cm/s is
(1) 20
(2) 30
(3) 50
(4) 80

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Solution

Dear Student ,
Here in this case ,
$D i s \tan c e t r a v e l l e d b y t h e p a r t i c l e i s t t h s e c o n d i s, S_{t} = u + \frac{1}{2} a (2 t - 1) . . . . (1) a n d t h e d i s \tan c e t r a v e l l e d i n (t + 1) s e c o n d i s, S_{t + 1} = u + \frac{1}{2} a (2 t + 2 - 1) = u + \frac{1}{2} a (2 t + 1) . . . . (2) S o t h e s u m o f t h e e q u a t i o n 1 a n d 2 i s, u + \frac{1}{2} a (2 t - 1) + u + \frac{1}{2} a (2 t + 1) = 100 \Rightarrow 2 u + \frac{1}{2} a [2 t - 1 + 2 t + 1] = 100 \Rightarrow 2 u + 2 a t = 100 \Rightarrow u + a t = 50 N o w a c c o r d i n g t o t h e e q u a t i o n o f m o t i o n ., v = u + a t = 50 c m / s$
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Q.2. A particle moving in a straight line inital velocity u and uniform acceleration f. If the sum of the distance travelled in tth and t+1th second is 100 cm, then its velocity after t seconds in cm/s is (1) 20 (2) 30 (3) 50 (4) 80

Q.2. A particle moving in a straight line inital velocity u and uniform acceleration f. If the sum of the distance travelled in $t^{t h}$ and ${(t + 1)}^{t h}$ second is 100 cm, then its velocity after t seconds in cm/s is
(1) 20
(2) 30
(3) 50
(4) 80