Question

Consider an object whose initial displacement and velocity are both equal to zero with respect to a reference point X. The object accelerates in a straight line away from X according to the following function of time: a(t) = 2t where the instantaneous acceleration is expressed in meters per second squared, and the initial time is t = 0. How fast is this object moving with respect to point X at t = 3 s?

		A. 1.732 m/s
		B. 3 m/s
		C. 6 m/s
		D. 9 m/s

Answer 1

Here the initial displacement and initial velocities are zero ie, The object is initially at rest. Then it moves away from the reference point with a time dependent acceleration. Ie, a(t)=2t. Ie the object accelerates with twice the time on each instant. Because of this time dependent acceleration we can't use the normal equations of motion. So we know that the acceleration is the derivative of velocity. Then by integrating the acceleration with respect to the time we get the corresponding velocity . The detailed solution is shown below as an image  

So the velocity of the object mentioned in the question at t=3 seconds is 9 m/s. Ie , option D) is the correct answer.