Question

An object's position is given by the equation X(t)=4.7−17t+162, in which X is in meters and t is in seconds. Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer 0.

A) There is an instant when the velocity is zero, and t=8.5 seconds.
B) There is an instant when the velocity is zero, and t=9.5 seconds.
C) There is no instant when the velocity is zero; answer 0.
D) There is an instant when the velocity is zero, and t=10.5 seconds.

Answer 1

The velocity of the object described by X(t)=4.7−17t+162 is a constant -17 m/s, and therefore, there is no instant when the velocity is zero.

Step-by-step explanation:

To determine if there is ever an instant when the velocity of the object is zero, we must first find the velocity function by differentiating the position function X(t). For the equation X(t) = 4.7 - 17t + 162, the velocity is the first derivative with respect to time t: v(t) = dX/dt = -17 (since 4.7 and 162 are constants and their derivatives are 0). As the velocity function v(t) is a constant -17 m/s and does not depend on time t, there is no instant when the velocity will be zero. It remains a constant -17 m/s at all times. Thus, the correct answer to the question about the object's velocity reaching zero is: C) There is no instant when the velocity is zero; answer 0.