Michael began driving a car on a straight track due north at t = 0 seconds. Afte
ID: 2884862 • Letter: M
Question
Michael began driving a car on a straight track due north at t = 0 seconds. After 6 seconds he stopped the car and began driving in reverse, south, for another two seconds, and then he stopped again. The graph below gives the velocity of the car, in meters per second, for the 8 seconds while Michael was driving it vtt) a) From the information you have been given, make an argument as to whether or not Michael passed over his original starting location while he was driving in reverse. b) Give an expression, in terms of VCt), that would give Michael's change in position over the 8 seconds time period he was driving.Explanation / Answer
(a)
The area under the velocity time graph gives the distance travelled. So for the first 6 seconds, the area under the v(t) plot from t=0 to t=6 gives the distance travelled in the forward direction.
Similarly, the area under the plot from t=6 to t=8 gives the distance travelled in the reverse direction.
Clearly, the area for the reverse direction is much greater than the area for the forward direction. So this means that Michael passed over his original location while driving in the reverse direction.
(b)
Let's represent the change in position by dS.
So,
dS = V(t)*dt
This is the required expression. Integrate the above expression within proper limits to find the position at any point of time during the first 8 seconds.