Question

part 3: graphs (10 points) question: make sure to label all axis and include all units for full points. the object started at time 0 and velocity of 0. when it is 2 seconds, the object has a velocity of 4m/s upward. when it is 8 seconds, the object has a velocity of 10m/s upward. find the acceleration of the object at 0 - 2 seconds and 2 - 8 seconds. find the total displacement of the object at the end of the trip. box your 3 answers with units.

Explanation:

Step1: Calculate acceleration from 0 - 2 seconds

Acceleration formula is $a=\frac{\Delta v}{\Delta t}$. Here, $v_0 = 0m/s$, $v_1=4m/s$, $t_0 = 0s$, $t_1 = 2s$. So $a_1=\frac{v_1 - v_0}{t_1 - t_0}=\frac{4 - 0}{2-0}=2m/s^2$.

Step2: Calculate acceleration from 2 - 8 seconds

$v_2 = 4m/s$, $v_3=10m/s$, $t_2 = 2s$, $t_3 = 8s$. So $a_2=\frac{v_3 - v_2}{t_3 - t_2}=\frac{10 - 4}{8 - 2}=1m/s^2$.

Step3: Calculate total displacement

The displacement in the first 2 - second interval (using $x_1=v_0t+\frac{1}{2}a_1t^2$, with $v_0 = 0$) is $x_1=\frac{1}{2}\times2\times2^2 = 4m$.
The displacement in the 2 - 8 second interval (using $x=v_2t+\frac{1}{2}a_2t^2$, where $v_2 = 4m/s$, $t=6s$, $a_2 = 1m/s^2$) is $x_2=4\times6+\frac{1}{2}\times1\times6^2=24 + 18=42m$.
The total displacement $x=x_1 + x_2=4+42 = 46m$.

Answer:

Acceleration from 0 - 2 seconds: $2m/s^2$
Acceleration from 2 - 8 seconds: $1m/s^2$
Total displacement: $46m$