Applications Of Derivatives Question 171
Question: Moving along the x-axis are two points with $ x=10+6t;x=3+t^{2}. $ The speed with which they are reaching from each other at the time of encounter is (x is in cm and t is in seconds)
[MP PET 2003]
Options:
A) 16 cm/sec
B) 20 cm/sec
C) 8 cm/sec
D) 12 cm/sec
Show Answer
Answer:
Correct Answer: C
Solution:
Time of encounter $ 10+6t=3+t^{2} $
therefore $ t^{2}-6t-7=0 $ , $ t=7 $ sec. At $ t=7\sec $ ., $ v_1=\frac{d}{dt}(10+6t)=6, $ cm/sec At $ t=7\sec . $
$ v_2=\frac{d}{dt}(3+t^{2})=2t=2\times 7=14 $ cm/sec \Resultant velocity = $ v_2-v_1=14-6=8, $ cm/sec
BETA
