Question

The acceleration of a particle is given by the relation a=90-6x^2 where a ios expressed in cm/s^2 and x in cm.if the particle starts with zero initial velocity at position x=0,determine,the velocity when x=5cm.the position where velocity is again in zero

Answer 1

Answer:

the formula of velocity will be there and pls follow me

Answer 2

Answer:

The velocity when x = 5cm is 200cm/s.

Explanation:

The acceleration of the particle is given to be a = 90 - 6x²

We know that acceleration is the change in velocity w.r.t time, i.e., a = dv/dt

a = dv/dt

a dt = dv

∫dv = ∫a dt

Since ∫dv = v, therefore

v = ∫a dt

v = ∫(90 - 6x²) dt

v = 90x - (6x³)/3

v = 90x - 2x³

Hence, velocity is given by v = 90x - 2x³

Velocity when x = 5cm is:

v = 90(5) - 2(5)³

v = 450 - 2(125)

v = 450 - 250

v = 200 cm/s

Therefore, the velocity at x=5cm is 200cm/s.

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