The velocity of a particle moving in straight line depends on its position as v= 3sin [(pi /2) + x ] m/s. Find the acceleration of the particle when at x = pi / 4. (Ans : -9/2 m/s)
Given,
v = 3 sin(π/2 +x)
=> v = 3 cos(x)
=> a = dv/dt = -3 sin(x) dx/dt
=> a = -3v sin(x)
=> a = -3[3 cos(x)] sin(x)
=> a = -(9/2) sin(2x)
Thus,
[a]π/4= -(9/2) sin(π/2) = -(9/2) m/s2