Question

which one of the following situations does the object have no acceleration? a) an elevator in a tall skyscraper moves upward at a constant speed of 3 m/s. b) seeing a red traffic light ahead, the driver of a minivan steps on the brake. as a result, the minivan slows from 15 m/s to stop before reaching the light. c) a boulder starts from rest and rolls down a steep mountain. d) a ball at the end of a string is whirled in a horizontal circle at a constant speed.

Explanation:

• Option a: When an object moves at a constant speed (in a straight - line, which is the case for an elevator moving upward at a constant speed), the change in velocity (\(\Delta v=v - u\), where \(v = u\)) is zero. Since acceleration \(a=\frac{\Delta v}{\Delta t}\), if \(\Delta v = 0\), then \(a = 0\).
• Option b: The minivan slows down. Its initial velocity \(u = 15\ m/s\) and final velocity \(v=0\ m/s\). So, \(\Delta v=v - u=- 15\ m/s\). Since \(\Delta v

eq0\), \(a=\frac{\Delta v}{\Delta t}
eq0\) (negative acceleration or deceleration).

• Option c: The boulder starts from rest (\(u = 0\)) and rolls down. Its velocity changes as it moves down the mountain (\(\Delta v

eq0\)), so \(a=\frac{\Delta v}{\Delta t}
eq0\).

• Option d: Although the ball has a constant speed in a circular motion, its direction of velocity is constantly changing. Velocity is a vector quantity. So, \(\Delta v

eq0\) (because of the change in direction), and \(a=\frac{\Delta v}{\Delta t}
eq0\) (centripetal acceleration).

Answer:

A. An elevator in a tall skyscraper moves upward at a constant speed of 3 m/s.