A particle moving along x-axis solution and explanation

This article answers the question “A particle moving along x-axis has acceleration f, at time t, given f=f nod(1-t/T), where f nod and T are constants. The particle at t=0 has zero velocity. When f=0, the particle’s velocity is?”

A particle moving along x-axis

A particle moving along x-axis has acceleration f, at time t, given f=f nod(1-t/T), where f nod and T are constants. The particle at t=0 has zero velocity. When f=0, the particle’s velocity is?

Ques: A particle moving along x-axis has acceleration f, at time t, given f=f nod(1-t/T), where f nod and T are constants. The particle at t=0 has zero velocity. When f=0, the particle’s velocity is?

Answer: The Particle’s velocity is-

1/{2}f_0T

Explanation:

Given that:

f~=~f_0(1~-~t/{T})

At zero acceleration

f~=~0

hence

f_0(1~-~t/{T})~=~0

1~-~t/{T}~=~0

t~=~T

Now, as we know that

acceleration~=~f~=~{dv}/{dt}

Hence:

{dv}/{dt}~=~f_0(1~-~{t/T})

integrating both sides

int{}{}{dv}~=~int{}{}f_0(1~-~{t/T})dt}

v~=~f_0t~-~{f_0t^2}/{2T}

At zero acceleration

t~=~T

hence

v~=~f_0t~-~{f_0t^2}/{2t}

v~=~f_0t~-~{f_0t}/{2}

v~=~1/{2}f_0t

Also see:

Three blocks with masses m 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m?Solve 24x 100 when x is a Natural Number

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