A particle moves in a straight line through a fixed point O with a velocity (4-t)m/s find an expression for its displacement S from this point given that S=S when t=0
S = 4t - (1/2)t^2 + c
"given that S=S when t=0" ?????
I will assume you meant: given that S=0 when t=0
0 = 0 - 0 + c ---> c = 0
S = 4t - (1/2)t^2
To find an expression for the particle's displacement from the fixed point O, we need to integrate its velocity function. The velocity function is given as (4-t) m/s.
Let's integrate the velocity function to get the expression for displacement S:
∫(4-t) dt
To integrate the function, we can use the power rule of integration:
∫(4-t) dt = ∫4 dt - ∫t dt
The integral of a constant is the constant times the variable:
∫4 dt = 4t
The integral of t with respect to t is (t^2)/2:
∫t dt = (t^2)/2
Combining the integrals, we have:
∫(4-t) dt = 4t - (t^2)/2
Now, to find the value of displacement S, we replace t in the expression for displacement with the given value when t=0:
S = 4t - (t^2)/2
S = 4(0) - (0^2)/2
S = 0
Therefore, when t=0, the particle's displacement from the fixed point O, S, is 0.
The final expression for the displacement S from the fixed point O is:
S = 4t - (t^2)/2