Basic kinematics variables using calculus: The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? A) 18.0 m/s B) 54.0 m/s C) 0.00 m/s D) 15.0 m/s E) 108 m/s

Question

Quizplus · Accepted Answer

We can find the velocity of the object at time t = 6.00 s by taking the integral of the acceleration function from t = 0.00 s to t = 6.00 s:

v(t) = ∫a(t)dt = ∫(3.00 m/s^2)t dt
v(t) = (3.00 m/s^2)(t^2/2) + C

Using the initial condition that the object is at rest at time t = 0.00 s, we know that the constant C = 0. Therefore:

v(6.00 s) = (3.00 m/s^2)(6.00 s^2/2) = 54.0 m/s

So the velocity of the object at time t = 6.00 s is 54.0 m/s. The best choice is B.

Basic Kinematics Variables Using Calculus: the Acceleration of an Object