Physics

Problem

A small drone travels along a straight line that we define as the positive

x

-axis (forward direction). The drone’s velocity is measured at three different clock readings: • At

t=0\,\text{s}

v=+2.0\,\text{m}\,\text{s}^{-1}

. • At

t=5.0\,\text{s}

v=+8.0\,\text{m}\,\text{s}^{-1}

. • At

t=12.0\,\text{s}

v=-3.0\,\text{m}\,\text{s}^{-1}

(the drone is now moving backward along the

x

-axis). Assume that between these clock readings the velocity changes uniformly during each interval, but the acceleration need not be the same in the two intervals. (a) Determine the average acceleration of the drone during the first interval from

t=0\,\text{s}

t=5.0\,\text{s}

. (b) Determine the average acceleration of the drone during the second interval from

t=5.0\,\text{s}

t=12.0\,\text{s}

. (c) Calculate the overall average acceleration of the drone for the entire

0\text{–}12\,\text{s}

time period. (d) Assuming the acceleration found in part (b) remained constant throughout the

5.0\text{–}12.0\,\text{s}

interval, derive an algebraic expression for the instant

t_0

(measured from

t=5.0\,\text{s}

) at which the drone momentarily came to rest before reversing direction. Then compute the numerical value of

t_0

Intuitive explanation

This problem asks you to find acceleration in each time interval using the definition $a = \Delta v / \Delta t$ . The key insight is that "uniform velocity change" means constant acceleration within each interval, so you can treat the two segments (0–5 s and 5–12 s) separately. Notice the drone switches from moving forward to backward, which will show up as different accelerations in each phase—calculate them independently, then you'll have the full picture of the motion.

Intuitive explanation

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