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Position of a particle moving on a 1D line is given by the equation:
3
f(t) = 2t - 21t + 60t
2
a) What is the velocity after 3s and after 6s b) When is the particle at rest c) When is the particle moving in the positive direction d) What is the total distance travelled by the particle during the first 6s
a)
fâ(t) = 6t - 42t + 60
2
fâ(3) = -12 fâ(6) = 24
b)
fâ(t) = 0
6t - 42t + 60 = 0
2
6(t - 5)(t - 2) = 0
t = 5, 2
c)
6(t - 5)(t - 2) > 0
t < 2
2 < t < 5
t > 5
6(t - 5)(t - 2)
Test
0 < x < 2 U t > 5
d) distance = | f(2) - f(0) | + | f(5) - f(2) | + | f(6) - f(5) |
- all the critical values
= 52 + 27 + 11 = 90