Answer:
When acceleration = 0,
velocity = 1
position = - 5
Step-by-step explanation:
The displacement of the particle is given by the equation
s(t) = t³ - 3t² + 4t - 7
The velocity equation can be determined by taking the first derivative which is the displacement per second
v(t) = s'(t) = d/dt( t³ - 3t² + 4t - 7) = 3t² - 6t + 4
The acceleration equation is obtained by taking the first derivative of v(t) which is the rate of change of velocity per second
a(t) = v'(t) = s"(t) = d/dt(3t² - 6t + 4) = 6t - 6
When acceleration is 0 we get a(t) = 0
6t - 6 = 0
6t = 6
t = 1 second
At t = 1, to find v(1) substitute t = 1 into
v(t) = 3t² - 6t + 4
v(1) = 3(1)² -6(1) + 4 = 3 - 6 + 4 = 1
s(1) = 1³ - 3 x 1² + 4 x 1 - 7
= 1 - 3 + 4 - 7
= 5 - 10
= -5