Question

Use the graph below for questions 11 15. Velocity versus Time 10 123 45678910 Time (s) 12. What is the instantaneous acceleration at t = 2 s? 13. What is the displacement from t3s tot 6s? 14. For what time interval(s) is the acceleration a. zero? b. positive? C. negative?

Answer 1

12. From observing the graph, we can see that from t=0s to t=3s, the graph has the same slope. If we can find that slope then, that value will be the acceleration at any time in between, since

$a=\frac{\mathrm{d} v}{\mathrm{d} t}=\text{slope}=\frac{\Delta v}{\Delta t}$

From the graph, in between 0s and 3s,

$a=\frac{\Delta v}{\Delta t}=\frac{6-1}{3-0}=\frac{5}{3}=1.66m/s^2$

_____________________________

13. Between 3s and 6s, the curve is flat, ie there is no acceleration and the velocity is constant which also means that we have a uniform motion in our time interval, the displacement during this time interval is given by the equation:

$\Delta x =v\Delta t$

$\Delta t$ is the time interval, here v=6m/s

Hence, $\Delta x=v\Delta t=6\times (6-3)=18m$

______________________________

14. a) As we have seen in the previous case, the acceleration is zero in the time interval t=3s to t=6s, since the slope in this time interval is zero

b)The acceleration is positive when the slope is positive (ie, the velocity is increasing with time), the time periods with the said attributes are, t=0s to t=3s and t=6s to t=8s

c) The acceleration is negative when the slope is negative (ie, the velocity is decreasing with time), the time periods with the said attributes is, t=8s to t=10s