Answer:
t=1.33333 seconds
Explanation:
1. We are give the the position function, s(t). We must differentiate s(t) twice in order to find the acceleration function, a(t).
s(t) = t⁶-2t⁵
Taking the power rule to differentiate s(t), we find the velocity function, v(t).
v(t) = d/dt (t⁶-2t⁵)
v(t) = 6t⁵-10t⁴
Differentiate v(t) using the power rule again to find the acceleration function, a(t).
a(t) = d/dt (6t⁵-10t⁴)
a(t) = 30t⁴-40t³
2. To find the other t value where acceleration is equal to zero, we must set a(t) to zero.
a(t) = 30t⁴-40t³ = 0
3. Algebraically solve for t. Factoring out 10t³ from a(t), we have:
10t³(3t-4)=0
Our solutions are t=0 and t=4/3.
The other value of t when acceleration is equal to zero is 4/3, or 1.33333 seconds.