A point moves along a straight line in such a way that after t seconds

1.	A point moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. (i) Find the average velocity of the points between t = 3 and t = 6 seconds. (ii) Find the instantaneous velocities at t = 3 and t = 6 seconds.
Answer» (i) Given s = 2t² + 3t (i.e.) f(t) = 2t² +3t Now f(3) = 18 + 9 = 27 = f(a) f(6) = 72 + 18 = 90 = f(b) Now (f(b) - f(a))/(b - a) = (90 - 27)/(6 - 3) = 63/3 = 21m/s (ii) f(t) = 2t² + 3t f'(t) = 4t + 3 f'(3) = 4(3) + 3 = 15 f'(6) = 4(3) + 3 = 15

A point moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. (i) Find the average velocity of the points between t = 3 and t = 6 seconds. (ii) Find the instantaneous velocities at t = 3 and t = 6 seconds.

Answer»

(i) Given s = 2t² + 3t

(i.e.) f(t) = 2t² +3t

Now f(3) = 18 + 9 = 27 = f(a)

f(6) = 72 + 18 = 90 = f(b)

Now (f(b) - f(a))/(b - a) = (90 - 27)/(6 - 3) = 63/3

= 21m/s

(ii) f(t) = 2t² + 3t

f'(t) = 4t + 3

f'(3) = 4(3) + 3 = 15

f'(6) = 4(3) + 3 = 15