Question

A particle moves along X-axis and its displacement at any time is given by x(t)=2t³ −3t² +4t in SI units. The velocity of the particle when its acceleration is zero, is

Answer 1

The velocity of the particle when its acceleration is zero is 1.5 m/s.

Step-by-step explanation:

To find the velocity of the particle when its acceleration is zero, we need to differentiate the displacement function with respect to time. Taking the derivative of x(t) = 2t³ - 3t² + 4t, we get the velocity function v(t) = 6t² - 6t + 4. To find the time when the acceleration is zero, we need to differentiate the velocity function with respect to time. Taking the derivative of v(t), we get the acceleration function a(t) = 12t - 6. Setting a(t) = 0 and solving for t, we find t = 0.5 seconds. Substituting this value back into the velocity function, we find that the velocity of the particle when its acceleration is zero is v(0.5) = 6(0.5)² - 6(0.5) + 4 = 1.5 m/s.