(Q.4) An object moving in a straight line travels s(t) kilometers in t​ hours, where s(t) = 7t^2 + t.

Question

​(a) What is the​ object's velocity when t = 6​? _______ (Answer).

​(b) How far has the object traveled in 6 hours? _______ (Answer).

​(c) When is the object traveling at a rate of 6 km/h? _______ (Answer).

Answer 1

S = 7t² + t

dS/dt = d/dt( 7t² +t) = Velocity = V

V= 14t +1

For V at t = 6 hour

(a) V(6) = 14*6+1 = 84+1 = 85 km/hr

(b) For distance travelled in 6 hours

S (6)= 7*36 +6 = 258 Km

(c) For Velocity as 6 K/hr

6 = 14t +1

5 = 14 t

t= 5/14 hr = 5*60 /14 min = 21.43 min or 0.357 hr