zaiden received the following problem: a particle moves in a straight line with velocity v(t) meters per…

zaiden received the following problem: a particle moves in a straight line with velocity v(t) meters per second (graphed), where t is time in seconds. at t = 6, the particles distance from the starting point was 5 meters in the positive direction. what is the particles displacement between t = 6 and t = 9 seconds? which expression should zaiden use to solve the problem?

zaiden received the following problem: a particle moves in a straight line with velocity v(t) meters per second (graphed), where t is time in seconds. at t = 6, the particles distance from the starting point was 5 meters in the positive direction. what is the particles displacement between t = 6 and t = 9 seconds? which expression should zaiden use to solve the problem?

Answer

Explanation:

Step1: Recall displacement - velocity relation

Displacement from $t = a$ to $t = b$ is given by $\int_{a}^{b}v(t)dt$. Here $a = 6$ and $b = 9$.

Step2: Write the required integral

The expression for the particle's displacement between $t = 6$ and $t=9$ seconds is $\int_{6}^{9}v(t)dt$.

Answer:

$\int_{6}^{9}v(t)dt$