Question

the graph of an objects velocity versus time is shown below. the y axis is velocity measured in meters per second and the x axis is the time measured in seconds. notice that each time increment is 5 seconds on the graph. determine the acceleration of the object during the time span from 0 seconds to 10 seconds.

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Step2: Determine initial and final velocities

At $t = 0\ s$, $v_0=0\ m/s$ (from the graph). At $t = 10\ s$, $v = 60\ m/s$. So, $\Delta v=v - v_0=60 - 0=60\ m/s$.

Step3: Calculate change in time

$\Delta t=10 - 0 = 10\ s$.

Step4: Calculate acceleration

$a=\frac{\Delta v}{\Delta t}=\frac{60}{10}=6\ m/s^{2}$.

Answer:

$6\ m/s^{2}$