Question

a particle moves along the -axis so that at time its position is given by . over the time interval , for what values of is the speed of the particle increasing? responses

Answer 1

The speed of the particle is increasing when the velocity is less negative and the acceleration is positive.

In order to determine the values of t for which the speed of the particle is increasing, we need to examine the given velocity function and its derivative, which is the acceleration function. Let's call the velocity function v(t). The speed of the particle is given by the absolute value of the velocity, so we can say that the speed is increasing when the acceleration is positive, regardless of the negative sign in the velocity function.

Based on the provided information, we know that the velocity function at t = 5 s is v(5 s) = -25 m/s. Since the acceleration is increasingly negative between t = 3 s and t = 5 s, the velocity is becoming less negative and eventually reaches zero. After that, the velocity becomes negative, indicating a change in direction. Therefore, the speed of the particle is increasing when the velocity is less negative and the acceleration is positive.