A particle moves in a straight line through a fixed point O with velocity (4-t)m/s find an expression for its displacement S from this point given that S=5 when t=0
well, just use Reiny's solution, plugging in 5 where he used 0 for S.
To find the expression for the displacement of the particle from point O, we can use the definition of velocity and integrate it with respect to time.
The velocity of the particle is given by (4-t) m/s.
Integrating velocity gives us the displacement. To do this, we integrate (4-t) with respect to t:
∫(4-t) dt = ∫4 dt - ∫t dt = 4t - (t^2/2) + C,
where C is the constant of integration.
Since we are given that the displacement is 5 when t is 0, we can substitute these values into the expression and solve for C.
When t is 0, S is 5:
5 = 4(0) - (0^2/2) + C,
5 = 0 - 0 + C,
C = 5.
Substituting C = 5 back into the expression for displacement:
S = 4t - (t^2/2) + 5.
Therefore, the expression for the displacement S of the particle from point O is S = 4t - (t^2/2) + 5.