Question

What is the time taken by the particle to cover a distance of 98 meters, if the particle is moving with a velocity given by,  \(\frac{dx}{dt}= \frac{1}{x} \)  (x is the distance)?

(a) 48 s

(b) 50 s

(c) 98 s

(d) 49 s

I have been asked this question in a job interview.

Origin of the question is Geometrical Applications in division Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

Correct answer is (d) 49 s

To explain I would say: Given: \(\frac{dx}{dt}= \frac{1}{x} \)

dt=xdx

Integrating, \(∫dt=∫_0^{98}xdx\)

\(t= (\frac{x^2}{2})_0^{98}=\frac{98}{2}=49 s\)