PLEASE PLEASE PLEASE HELP! I don\'t understand how to do A and B PLEASE PLEASE P

Question

PLEASE PLEASE PLEASE HELP! I don't understand how to do A and B

PLEASE PLEASE PLEASE HELP! I don't understand how to do A and B

1. A particle moves along the x-axis so that its velocity at time osts 12, is given by a differentiable function v whose graph is shown at the right. The velocity graph consists of a semicircle and two line segments. 3 5 6 7: 8: 9. 10 12 (a) At what time. 0 Sts 12, is the speed of the particle the greatest? (b) At what times, if any, does the particle change direction? Explain briefly (c) Find the total distance traveled by the particle from time t 0 to t 12. (d) If the initial position of the particle is x(0) 2, find the position of the particle at time

Explanation / Answer

A.

There is a minute difference between speed(s) and velocity(v) which is direction. Speed is always gonna be positive regardless of direction but velocity can be negative depends on the direction.

So we can say that s= |v|

Now where is the speed of the particle is greatest

v(t=2) = 2 so speed is s = 2

v(t=8) = -3, speed is s = |-3|=3

so answer is t=8

B.

Particle change direction exactly when velocity is negative. Because I have already mentioned above that velocity takes care of direction.

so particle is going to change its direction at t = 4

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