Consider a particle moving along a straight line, whose position as a function of time is given by s(t) = t2 - t + , where = 1 m s-2, = 6 m s-1 and = 5 m. The average speed of the particle, in m s-1 from t = 0 to t = 6 s is:
- 0
- 12
- 6
- 3
Answer
(4) 3
Solution
Given s(t) = t2 - 6t + 5.
Velocity of the particle is v(t) = dsdt = 2t - 6.
The particle reverses its direction of motion when v(t) = 0 t = 3 s.
Positions at relevant times:
s(0) = 5 m
s(3) = (3)2 - 6(3) + 5 = -4 m
s(6) = (6)2 - 6(6) + 5 = 5 m
Distance covered in t = 0 to 3 s:
d1 = |s(3) - s(0)| = |-4 - 5| = 9 m
Distance covered in t = 3 to 6 s:
d2 = |s(6) - s(3)| = |5 - (-4)| = 9 m
Total distance travelled:
d = d1 + d2 = 9 + 9 = 18 m
Total time taken t = 6 s.
Average speed:
vavg = Total distanceTotal time = 186 = 3 m s-1
Answer: (4)