Question

The position of a particle as a function of time is given by equation: x=2t3−6t2+12t+6. The acceleration of the body is zero at

Answer 1

Final Answer : 1s

STEPS :
1) The position of a particle as a function of time is given by equation
$x = 2 {t}^{3} - 6 {t}^{2} + 12t + 6 \\ \frac{dx}{dt} = v(t)= 6 {t}^{2} - 12t \\ \\ \frac{dv}{dt} = a (t)= 12t - 12 = 0 \\ 12t = 12 \\ = > t = 1s$

Therefore, At t= 1s the acceleration of the body is 0.

Answer 2

x = 2t³ - 6t² + 12t + 6

v = dx/dt = 6t² - 12t + 12

a = dv/dt = 12t - 12

If acceleration (a) is zero then

0 = 12t - 12

t = 1

∴ Acceleration is zero at t = 1