Question

if the velocity of a particle is given by v=✓180-16xm/s what will be its accelertion

Answer 1

If the velocity is v= √ (180-16x) m/s, then what is the acceleration?

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6 ANSWERS



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Answered Jul 28, 2017

We know that acceleration is rate of change of velocity.

We have, v=(180–16x)^1/2

Now,differentiating it w.r.t t i.e time,

So, dv/dt = [1/2(180–16x)^(-1/2)](-16dx/dt)

(I hope u have no problem in differentiating, if u have then please recinsider because it's basics)

So, on simplifying above equation,

a(acc.)=dv/dt=[1/2(180–16x)^(-1/2)](-16v)

Putting the value of v from original equation,

a=dv/dt=[-8(180–16x)^(-1/2)](180–16x)^1/2)

Clearly,on simplifying we get,

a=dv/dt=-8 m/sec^2 which is the required answer.

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Answer 2

v=√180-16x
differentiate both side
dv/dx = d(180-16x)^1/2/dx
dv/dx = 1/2(180-16x)^-1/2*-16
multiply by dt on L. H. S in numerator and denomerator
dv/dx * dt/dt = 1/2(180-16x)^-1/2*-16
dv/dt * dt/dx=1/2(180-16x)^-1/2*-16
a * 1/v = 1/2(180-16x)^-1/2*-16
a = 1/2√(180-16x)-16 * √(180-16x)
a = (1/2√(180-16x) -16(√180-16x) )/√180-16x*√180-16x
a = -16√180-16x/2
a= -8√180-16x.