Question

A particle moves along the x-axis so that at time t > o its position is given by xt) = 243 - 942 - 60t 4. What is the total distance traveled by the particle over the time interval 0 ≤ t ≤ 7?

1) 168
2) 171

Answer 1

The total distance traveled by the particle over the time interval 0 ≤ t ≤ 7 is 10920 units.

Step-by-step explanation:

To find the total distance traveled by the particle, we need to find the displacement at each time interval and then add up the magnitudes of these displacements. The displacement at a particular time interval can be found by taking the difference between the position at the end of the interval and the position at the start of the interval.

Let's calculate the displacement for the time interval 0 ≤ t ≤ 7:

Displacement = x(7) - x(0) = (243 - 942 - 60 * 7^4) - (243 - 942) = -60 * 7^4 = -10920

The total distance traveled is the absolute value of the displacement, so the answer is | -10920 | = 10920.