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

To find the velocity at time t=6s, we need to integrate the acceleration function from 0s to 6s:
v(t) = ∫[0,6] a(t) dt = ∫[0,6] (3.00t) dt
v(t) = 1.5t^2 + C   (where C is the constant of integration)
Since the object is at rest at t=0, we know that the initial velocity is 0 m/s. Therefore, we can solve for C:
0 = 1.5(0)^2 + C 
C = 0 
Thus the velocity function is: v(t) = 1.5t^2 
The velocity at t=6s is:
v(6) = 1.5(6)^2 = 54.0 m/s
Therefore, the correct answer is B.

The Acceleration of an Object as a Function of Time