Question

The motion of a particle is defined by the relation s=2t^3-15t^2 24t 4 where s is expressed in meters and t in seconds. determine (a) when the velocity is zero(b) the position and total distance traveled when the acceleration is zero

Answer 1

To solve kinematic problems in physics, velocity is determined by differentiating the displacement function with respect to time, and acceleration is found by differentiating the velocity function. When acceleration is zero, the corresponding position is found using the displacement function, and the total distance traveled is the integral of velocity over time.

Step-by-step explanation:

The question involves understanding the concepts of velocity and acceleration in physics, specifically within the context of kinematics. In kinematics, the motion of a particle is often described by equations that relate displacement (s), velocity (v), and acceleration (a) with time (t).

Part (a) of the problem typically involves taking the first derivative of the displacement function to find the velocity function and setting it to zero to determine when velocity is zero. For example, from the given displacement function s(t) = 2t3 - 15t2 + 24t + 4, the velocity function v(t) would be the derivative of s(t) with respect to time t.

Part (b) requires taking the second derivative of the displacement function to find the acceleration function and setting it to zero to determine when acceleration is zero, and then using the original displacement function to find the position of the particle at that particular time.

The total distance traveled is the integral of the absolute value of the velocity function over the time interval of interest.