Question

Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units of m/s.

a.) Determine when the motion is in the positive direction and when it is in the negative direction.
b.) Find the displacement over the given interval.
c.) Find the distance traveled over the given interval
v(t) = 3t²-36t+105; [0,8]

Answer 1

To determine when an object's motion is positive or negative, analyze the sign of the velocity function. Displacement is found by integrating the velocity over the time interval. Distance traveled is the integral of the velocity's absolute value.

Step-by-step explanation:

To determine when the motion is in the positive or negative direction, we look at the given velocity function v(t) = 3t² - 36t + 105. The motion is in the positive direction when v(t) is positive and in the negative direction when v(t) is negative. To find the displacement over the interval [0,8], we would integrate v(t) from 0 to 8 seconds. To find the distance traveled, we integrate the absolute value of v(t) over the same interval, taking into account any changes in direction.

For part (b) and (c), we would perform the necessary integration. Unfortunately, without specific calculations or further details, we cannot provide a numerical answer here.