As in the case of multiple choice questions, free response questions in the AP Physics Exams are designed to test your knowledge, understanding and capability for applying the things you have studied. But unlike the multiple choice questions, the presentation of the answers of free response questions is very important since you have to give all the required details in an effective manner within the stipulated time.

Here are two free response practice questions on kinematics. Question No.1 is for AP Physics B; but it will be useful for AP Physics C aspirants also. ** Question No.2 is for AP Physics C only**.

**(1)** Points A, B and C lie on a straight line parallel to the X-axis in a region of space where a small uniform electric field **E** directed along the negative X-direction exists. Other fields (including gravitational field) are negligible. A proton of mass *m* and charge *e *is projected from point B with velocity *u* along the *positive *X-direction.

A………….B………………..C

Now, answer the following questions:

**(a)** Draw a graph to indicate qualitatively the nature of variation of the displacement of the proton with time from the instant of projection to the instant it returns to the point of projection. (Take the time *t* along the X-axis and the displacement *s *along the Y-axis). Explain why the shape of the graph is as shown by you.

**(b)** Draw a graph to indicate qualitatively the nature of variation of the velocity of the proton with time from the instant of projection to the instant it returns to the point of projection. (Take the time *t* along the X-axis and the velocity *v *along the Y-axis). Explain why the shape of the graph is as shown by you.

**(c)** Determine the time *T* required for the proton to attain the *maximum* displacement BC and indicate this time *T* in the velocity–time graph.

**(d) **Determine the maximum displacement BC.

**(e)** Another proton was projected simultaneously from point B with the same speed *u* along the *negative* X-direction. The first proton arrived at the point A in time *t*_{1 }and the second proton in a shorter time *t*_{2}. If a third proton is released (from rest) at the point B, determine the time required for it to reach the point A.

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**(2) **An iron ball of mass *m *released from rest at time *t =* 0 from a stationary balloon at a height falls under gravity which can be assumed to be constant. While falling down, the ball experiences a viscous drag force *D *(due to the air) in the form *D = *– *bv *where *v* is the velocity of the ball and *b *is a constant. Now answer the following questions in this context:

**(a)** Assuming that the acceleration due to gravity *g *is constant throughout the path of the ball, draw a graph to indicate the nature of variation of the acceleration of the ball with its velocity. Take the velocity *v* along the X-axis and the acceleration *a *along the Y-axis. Incorporate all possible values of velocity in the graph and give the reason for the shape of the graph.

**(b) **Write a differential equation for the acceleration of the ball.** *** *

**(c) **Solve the differential equation you have written in part (b) to obtain the time-dependent velocity of the ball in terms of the given parameters and fundamental constants.

**(d) **From the expression for the velocity obtained in part (d) obtain the terminal velocity of the ball.

**(e) **If the ball were moving through water instead of air,* *how would the terminal velocity be affected? Put a tick mark against the correct statement out of (i), (ii) and (iii) given below:

(i) Terminal velocity will be unchanged ___

(ii) Terminal velocity will be increased ___

(iii) Terminal velocity will be decreased ___

Justify your answer giving two important reasons.

The above questions carry 15 points each. You can take about 17 minutes for answering question No.1 and about 15 minutes for answering question No.2. Try to answer these questions. I’ll be back soon with model answers for your benefit.

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