The velocity of a particle moving along x - axis is given as #v = x^2 - 5x + 4#(in m/s), where x denotes the x-coordinate of the particle in meters. Find the magnitude of acceleration of the particle when the velocity of particle is zero?

A: #0m/s^2#
B: #2m/s^2#
C: #3m/s^2#
D: None of the above

Answer 1

A

Given velocity #v=x^2−5x+4# Acceleration #a-=(dv)/dt#
#:.a=d/dt(x^2−5x+4)# #=>a=(2x(dx)/dt−5(dx)/dt)#
We also know that #(dx)/dt-=v#
#=>a=(2x −5)v#
at #v=0# above equation becomes #a=0#
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Answer 2

The magnitude of acceleration when the velocity of the particle is zero can be found by differentiating the velocity function with respect to time (t) to find the acceleration function, and then plugging in the value of x when v = 0 into the acceleration function.The acceleration function (a) can be found by differentiating the velocity function (v) with respect to time (t):

[ a = \frac{dv}{dt} = \frac{d}{dt}(x^2 - 5x + 4) ]

[ a = \frac{d}{dt}(x^2) - \frac{d}{dt}(5x) + \frac{d}{dt}(4) ]

[ a = 2x\frac{dx}{dt} - 5\frac{dx}{dt} + 0 ]

[ a = 2xv - 5v ]

Now, when the velocity of the particle is zero, ( v = 0 ), so:

[ a = 2x(0) - 5(0) ]

[ a = 0 ]

Therefore, the magnitude of acceleration of the particle when the velocity is zero is 0 m/s².

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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