Question

Find the distance travelled by a car moving with acceleration given by a(t)=t^2 – t, if it moves from t = 0 sec to t = 1 sec, if velocity of a car at t = 0sec is 10 km/hr.

(a) ^119⁄22 km

(b) ^119⁄15 km

(c) ^129⁄12 km

(d) ^119⁄12 km

I have been asked this question in my homework.

I want to ask this question from Application of Double Integrals topic in division Multiple Integrals of Engineering Mathematics

Answer 1

Right choice is (b) ^119⁄15 km

Easy explanation: Add constant automatically

We know that,

a=\(\int\int[t^2-t] dtdt=\int [\frac{t^3}{3}-\frac{t^2}{2}]dt=\int_0^1\left [\frac{t^3}{3}-\frac{t^2}{2}+10 \right ] dt=\left [\frac{t^4}{12}-\frac{t^3}{6}+10t\right ]\)

=\(\frac{1}{12}-\frac{1}{6}+10=\frac{1}{6} [\frac{1}{2}-1]+10 km=-\frac{1}{12}+10=\frac{119}{12}\)km