Velocity of a particle varies with time as v=t^2-t-2. average speed of the particle in time interval from t=0 to t=4sec?
2 Answers
The average speed is
Explanation:
The velocity as a function of time is
The average speed
3 m/s
No units for distance were given so I assumed meters.
Explanation:
The vt graph looks like this:
graph{x^2-x-2 [-10, 10, -5, 10]}
You can see that the particle is moving away from the origin at
t = 0 s. It then returns and moves away in a positive direction at
t = 2 s.
The question asks for the average speed which is a scalar quantity. This means we must find the total distance travelled as opposed to the displacement, which is a vector quantity.
To do this I will find the absolute value of the distance travelled between 0 and 2 s then add this to the absolute value of the distance travelled between 2 and 4 s.
In a vt graph the distance travelled is the area between the t axis and the line. We can find this by integration:
For the interval 0 to 2:
For the interval 2 to 4:
This is the total distance travelled.