Question 1 of 5 · Particle Kinematics · Foundation · About 12 min

Braking capsule in a resistive medium

A test capsule enters a resistive medium moving in the positive $x$ direction at $v_0=32\,\mathrm{m/s}$ . Its acceleration is $a_x(t)=-4t\,\mathrm{m/s^2}$ for . Determine its first stopping time and the distance travelled before coming to rest. Take .

A smooth rounded test capsule moving along a straight horizontal line, with the medium shown as a pale blue band around the line. A long dark blue arrow to the right of the capsule shows its entry velocity. A shorter dark red arrow to the left shows acceleration. A small +x arrow pointing right sits below the line. Labels: v0 = 32 m/s; a(t) = -4t; +x; resistive medium — Schematic, not to scale unless dimensions are given.

Given

$v_0=32$ m/s
$a_x=-4t$ m/s²

Find

Stopping time
Travelled distance

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

Independent Waypoint Mentor learning material. Not affiliated with or endorsed by any university.

Braking capsule in a resistive medium

Given

Find

Assumptions

Worked solution