To find the total distance traveled by the particle, we need to consider the displacement of the particle over different time intervals. The total distance is the sum of the absolute values of the displacements over different intervals. However, the time interval is not specified in the question, so we cannot calculate the total distance.
Step-by-step explanation:
To find the total distance traveled by the particle, we need to consider the displacement of the particle over different time intervals. The displacement is given by the difference in position at the end and the beginning of the time interval. So, we can find the displacement by subtracting the position at the end of the interval from the position at the beginning of the interval.
Let's calculate the displacement over the time interval from 0 to t.
At t=0, the position is s(0) = 3(0)^2 - 2(0) + 5 = 5. At t, the position is s(t) = 3t^2 - 2t +5.
The displacement over the time interval from 0 to t is given by s(t) - s(0) = 3t^2 - 2t +5 - 5 = 3t^2 - 2t.
Now, we need to find the total distance traveled by the particle, which is the sum of the absolute values of the displacements over different intervals. Since the time interval is not specified, we cannot calculate the total distance traveled by the particle.
The probable question can be:
a particle moves along the -axis so that at time its position is given by s(t)=3t² −2t+5. what is the total distance traveled by the particle over the time interval ? responses
a. 145
b. 180
c. 195
d. 233