A particle, moving in a straight line, passes through a fixed-point O. Its velocity vms -1 ,

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A particle, moving in a straight line, passes through a fixed-point O.

Its velocity vms-1, t seconds after passing through O, is given by v = k cos 4t, where k is a positive constant.

a. Find the value of t when the particle is first instantaneously at rest.

b. Find an expression for the acceleration, a, of the particle t seconds after passing through O.

c. Given that the acceleration of the particle is 10 ms-2 when t = 7π/24, find the value of k.

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