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the motion of a particle moving in a straight line is described by x=3 cos2t, where the symbol have their usual meaning determine the distance x , where the speed is zero
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the motion of a particle moving in a straight line is described by x=3...
Solution:

Distance where the speed is zero


The motion of a particle moving in a straight line is given by the equation x = 3cos2t, where x denotes the distance of the particle from a fixed point and t denotes the time elapsed.

The speed of the particle is given by the derivative of x with respect to time t.

v = dx/dt = -6sin2t

To find the distance where the speed is zero, we need to find the values of t for which v = 0.

-6sin2t = 0

sin2t = 0

2t = nπ, where n is an integer

t = nπ/2, where n is an integer

Substituting the values of t in the equation x = 3cos2t, we get:

x = 3cos(nπ)

For even values of n, cos(nπ) = 1

For odd values of n, cos(nπ) = -1

Therefore, the distance x where the speed of the particle is zero is given by:

x = 3 for even values of n

x = -3 for odd values of n

Thus, the distance where the speed is zero alternates between 3 and -3 as the particle moves along the straight line.

Therefore, the distance x where the speed is zero is given by the equation:

x = 3n, where n is an even integer

x = -3n, where n is an odd integer.
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the motion of a particle moving in a straight line is described by x=3 cos2t, where the symbol have their usual meaning determine the distance x , where the speed is zero
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