Question

An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function v = 4 + t2/2. The displacement of the object between t = 0 and t = 6 seconds is:

Answer 1

The displacement of an object whose velocity varies with time as v = 4 + t2/2 from t = 0 to t = 6 seconds is found by integrating the velocity function over that time period, representing the area under the velocity-time graph.

Step-by-step explanation:

When determining the displacement of an object with a velocity function v = 4 + t2/2, where t is time in seconds, and v is velocity in meters per second, we need to integrate the velocity function over the given time period, from t = 0 to t = 6 seconds.

The displacement is the area under the velocity versus time graph for the object's motion. By integrating the given function, we get the displacement as an antidifferentiation of the function:

∫ v dt = ∫ (4 + t2/2) dt

Integrating within the bounds from 0 to 6 seconds provides us the total displacement.

This is a typical example of an application of calculus in mechanics, which is a branch of physics dealing with motion.