A particle moves along a straight line such that its position is defined by s = (t3 – 3 t2 + 2 ) m. Determine the velocity of the particle when t = 4 s.
V = d/t = (t^3-3t^2+2)/4=(4^3-3*4^2+2)/4
= 4.5 m/s.
To determine the velocity of the particle at a specific time, we need to find the derivative of the position function with respect to time. In this case, the position function is given by:
s = t^3 - 3t^2 + 2
To find the velocity, we differentiate the position function with respect to time (t). So let's find the derivative:
ds/dt = d/dt(t^3 - 3t^2 + 2)
= 3t^2 - 6t
This derivative gives us the instantaneous rate of change of position with respect to time, which is the velocity.
Now, substitute t = 4s into the derivative to find the velocity when t = 4s:
v = 3(4)^2 - 6(4)
= 48 - 24
= 24 m/s
Therefore, the velocity of the particle when t = 4s is 24 m/s.