A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10^th second of its motion?

Category: QuestionsA particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10^th second of its motion?
Editor">Editor Staff asked 11 months ago

A particle moving in a straight line with uniform acceleration has a velocity 10 cm/sec and 8 seconds later has a velocity 54 cm/sec. What will be the described by the particle during the 10^th second of its motion?
 
(a) 38.5cm
 
(b) 37.5cm
 
(c) 38cm
 
(d) 39.5cm
 
I had been asked this question during an interview.
 
This is a very interesting question from Calculus Application in section Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Correct option is (a) 38.5cm
 
The best explanation: Let, the particle moving with a uniform acceleration of f cm/sec^2.
 
By question initial velocity of the particle is u = 10 cm/sec and its velocity after 8 seconds = v = 34 cm/sec.
 
Thus, using the formula v = u + ft we get
 
34 = 10 + f*8
 
Or 8f = 24
 
Or f = 3
 
Therefore, the required acceleration of the particle is 3 cm/sec^2.
 
The space described during the 10th second of its motion is,
 
= [10 + 1/2(3)(2*10 – 1)]   [using the formula st = ut +1/2(f)(2t – 1)]
 
= 10 + 28.5
 
= 38.5cm.