Question

A racer accelerates from a stop so that its speed is 10t m/s t second after starting how far will the car go in 4 seconds?

(a) 80m

(b) 60m

(c) 40m

(d) 160m

I have been asked this question in an interview.

My doubt stems from First Order First Degree Differential Equations topic in section Ordinary Differential Equations – First Order & First Degree of Engineering Mathematics

Answer 1

The correct option is (a) 80m

To explain I would say: Given \(\frac{dy(t)}{dt}=10t…\) where y(t) is the distance travelled a function of time above equation is a first order first degree DE where t varies from 0 to 4 seconds integrating on both side w.r.t t we get \(\int_0^4 dy(t) = \int_0^4 10t \,dt\)

\(= y(4)-y(0) = \big[5t^2\big]_0^4….. \) but y(0) = 0 since car is at rest at time t=o

y(4) = 5(16) = 80m.