Problem 1 An impatient person is walking at a constant speed in a circle as show

Question

Problem 1 An impatient person is walking at a constant speed in a circle as shown above (A-> B C- D ), starting from point A at time t-0. 'The center of the circle is at y1.5m, the radius of the circle is 1 m, and the person is walking with a speed of 1m/s Which is the correct plot oî the x coordinate of the person as a function of Lime? 2,5 1.5 1.5 0.5 0.5 0.5 .0.5 Which is the correct plot of the direction of the person's velocity, measured as an angle Va from the x axis, increasing counter-clockwise? 180° 90° 180° 90° 180 180° -180° -180° Which is the corect plot of the direction of the person's acceleration as a function of tine, masured as an angle aa from the x axis, increasing counter-clockwise 180 180° 180° Lec 0° 90° 90° -180° 90° -180° -180

Explanation / Answer

(a) First take the displacement of the person.

Intially the person is at a, means its distance from x-axis

= distance of the center of circle from x-axis + radius of the circle

= 1.5 m + 1.0 m = 2.5 m

Now, as the person moves from A to B, x- cordinate decreases and y - cordinate increases.

Again when the person moves from B to C, x decreases and y - increases in negative direction.

The same follows from C to D and D to A.

So, a sinusoidal wave type of graph is generated.

Hence the last one is the correct graph.

(b) For the direction of velocity -

When the person starts moving from point A to B, initial direction is 90 deg and it increases gradually and when the person reaches at point B, the direction becomes 180 deg.

From point C to D, the direction of velocity starts from -180 deg and reaches at + 180 deg at point D.

It continues till point A is reached.

Hence the third graph shows the correct velocity angle of the person's motion.

(c) Acceleration is the derivative of velocity means, there is 180 deg phase difference between the two.

Second graph shows correctly the phase difference of 180 deg from the velocity graph.

Hence it is the correct answer.

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