Question

a rock thrown vertically upward from the surface of the moon at a velocity of 8 m/sec reaches a height of s = 8t - 0.8t² meters in t sec. a. find the rocks velocity and acceleration at time t. b. how long does it take the rock to reach its highest point? c. how high does the rock go? d. how long does it take the rock to reach half its maximum height? e. how long is the rock aloft? a. find the rocks velocity at time t. v = 8 - 1.6t m/s find the rocks acceleration at time t. a = m/s² (simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Recall the relationship between velocity, acceleration and position

Velocity $v(t)$ is the derivative of position $s(t)$, and acceleration $a(t)$ is the derivative of velocity $v(t)$. Given $s(t)=8t - 0.8t^{2}$.

Step2: Find the velocity function

Differentiate $s(t)$ with respect to $t$ using the power - rule $\frac{d}{dt}(t^n)=nt^{n - 1}$. So $v(t)=\frac{d}{dt}(8t - 0.8t^{2})=8-1.6t$.

Step3: Find the acceleration function

Differentiate $v(t)$ with respect to $t$. Since $v(t)=8 - 1.6t$, then $a(t)=\frac{d}{dt}(8 - 1.6t)=- 1.6$.

Answer:

$-1.6$