The displacement, in metres of a ball rolling in a straight line on a grassy hill is given approixmately by?

Question

s=-t^2+6t+5, where t is measured in seconds. Find the average velocity over the following time period. t E [2,4].

Answer 1

Reading as :-
s(t) = t ² + 6t + 5
s(4) = 16 + 24 + 5 = 45
s(2) = 4 + 12 + 5 = 21
Average velocity = (45 - 21) / (4 - 2) m/s
Average velocity = 12 m/s

Answer 2

average velocity
= (1/2)∫s'(t) dt, from 2 to 4
= (1/2)∫-2t+6 dt, from 2 to 4
= 0

This means that the ball returns to its original position.

Answer 3

Differentiate displacement to get velocity

Answer 4

average velocity:

s(4) - s(2)
--------------
4-2

(-(4)^2 + 6(4) + 5) - (-(2)^2 + 6(2) + 5)
= ___________________________
4-2

13 - 13
=--------
2

= 0/2 = 0

so the average velocity = 0 m/s