Answer
(a)
Acceleration at time $t=5$ min is $-120\hspace{4px} m/s^{2}$.
(b)
The acceleration in the graph is negative. So, the helicopter is slowing down during this time interval.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/23dea384-9eb7-4530-bde4-b631c43be086/result_image/1620506855.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001857Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=caea919b0442d486e18d1e13fa7ec961419ce108d669b8db4815b074599db15b)
Work Step by Step
(a)
Firstly, calculate first derivative of $s(t) = 300t − 4t^{3}$ m using power rule.
$\dfrac{ds}{dt}=300-4\times3t^{2}$
Now calculate second derivative by differentiating on both side of equation $\dfrac{ds}{dt}=300-4\times3t^{2}$.
$\dfrac{d^{2}s}{dt^{2}}=0-4\times3\times2t=-24t$
Now, substitute $t = 5$ min and solve.
$\dfrac{d^{2}s}{dt^{2}}=-24\times 5=-120$
Since acceleration is the second derivative of displacement.
Acceleration at time $t=5$ min is $-120\hspace{4px} m/s^{2}$.
(b)
The acceleration in the graph is negative.
Thus, the velocity must be decreasing.
So, the helicopter is slowing down during this time interval.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/23dea384-9eb7-4530-bde4-b631c43be086/steps_image/small_1620506855.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001857Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=f3ee0a5e86ed3857b2ee11efe3ae41def1f88acfdd0fe5b908bb04cb766ffe7b)