1. a velocity function is given by v(t)= -3t² + 12t - 9. find the times when the object is stopped. a. t =…
1. a velocity function is given by v(t)= -3t² + 12t - 9. find the times when the object is stopped. a. t = 2,4 b. t = 1,3 c. t = 0,3 d. t = 1,2
Answer
Explanation:
Step1: Set velocity equal to 0
When the object is stopped, $v(t)=0$. So we set $-3t^{2}+12t - 9=0$.
Step2: Divide by - 3
Divide the entire equation by - 3 to simplify: $t^{2}-4t + 3=0$.
Step3: Factor the quadratic
Factor the quadratic equation: $(t - 1)(t - 3)=0$.
Step4: Solve for t
Set each factor equal to 0: $t-1 = 0$ gives $t = 1$; $t - 3=0$ gives $t=3$.
Answer:
B. $t = 1,3$