The acceleration of a particle is defined by the relation a 5 2kv2.5, where k is a constant. the particle starts at x 5 0 with a velocity of 16 mm/s, and when x 5 6 mm, the velocity is observed to be 4 mm/s. determine (a) the velocity of the particle when x 5

The velocity of the particle is 4.76 mm/s.

Explanation:

Given that,

At x = 0, v = 16 mm/s

At x = 6 mm, v = 4 mm/s

The equation of acceleration is

Here, k = constant

v= velocity

Th velocity of the particle along straight line

....(I)

The acceleration of the particle along a straight line

....(II)

From equation (I) and (II)

Put the value of a

On integrating

....(III)

Put the value of x = 0 and v = 16 mm/s in equation (III)

Now put the value of x = 6mm and v = 4 mm in the equation (III)

Put the value of k and C in equation (III)

We need to calculate the velocity of the particle when x = 5

Put the value in the equation

Hence, The velocity of the particle is 4.76 mm/s.

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