Kinematics Question 161
Question: A police party is chasing a dacoit in a jeep which is moving at a constant speed v. The dacoit’s on a motorcycle. When he is at a distance x from the jeep, he accelerates from rest at a constant rate. Which of the following relations is true if the police it’s able to catch the dacoit?
Options:
A) $ v^{2}\le \alpha x $
B) $ v^{2}\le 2\alpha x $
C) $ v^{2}\ge 2\alpha x $
D) $ v^{2}\ge \alpha x $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] If police it’s able to catch the dacoit after time t, then $ Vt=x+\frac{1}{2}at^{2} $ . this gives $ \frac{a}{2}t^{2}-vt+x=0 $ Or $ t=\frac{v\pm \sqrt{v^{2}-2\alpha x}}{\alpha } $ For t to be real, $ v^{2}\ge 2ax $
