A particle moves in a straight line. At time t seconds its velocity is given by v(t) = t2 + 2t - 8
m/s. Find an expression for the displacement s(t) from O at time t given that the initial position is
4 metres from the origin O (in the positive direction). Draw the motion diagram and find the
distance travelled in the first 3 seconds.
Solution
\\(v = ds/dt\\) Intergrate: \\( s = t^3/3 + t^2 -8t +c\\) Given that s at t-0 is 4, so c= 4.
\\( s(t) = t^3/3 + t^2 -8t + 4\\) \\( s(3) = 3^3/3 + 3^2 -8(3) + 4 = -2m\\).
Đề tieng anh thpt 2024 danh cho cac ban hoc sinh
A particle moves in a straight line. At time t seconds its velocity i.pdf
1. A particle moves in a straight line. At time t seconds its velocity is given by v(t) = t2 + 2t - 8
m/s. Find an expression for the displacement s(t) from O at time t given that the initial position is
4 metres from the origin O (in the positive direction). Draw the motion diagram and find the
distance travelled in the first 3 seconds.
Solution
(v = ds/dt) Intergrate: ( s = t^3/3 + t^2 -8t +c) Given that s at t-0 is 4, so c= 4.
( s(t) = t^3/3 + t^2 -8t + 4) ( s(3) = 3^3/3 + 3^2 -8(3) + 4 = -2m)
