if a particle moves along a horizontal path with an acceleration of a=(2t-9) m/s2 ( t is in seconds), determine the followings.

Question

A) velocity and position of particle at t=9s
B) total distnace travelled by particle
C) average velocity and average speed of the particle
at t=0 s=5m and Vo= 9m/s

Answer 1

a = dv/dt = 2t-9
v = ds/dt = t^2 - 9t + v₀
s = 1/3 t^3 - 9/2 t^2 + v₀t + s₀

fill these in, and the other questions should be easy. Come back with your work if you get stuck.

Answer 2

v = initial v + integral a dt
x = initial x + integral v dt
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v = 9 + integral a dt = t^2 - 9 t + 9
x = 5 + t^3/3 - (9/2)t^2 + 9 t