Kinematics and variable acceleration question

An object falls through a fluid so that the distance fallen, in metres, at time t seconds is given by s=40(4e^{^(-t/4)} + t - 4). Find the initial and terminal speeds of the object.
I am a bit stuck with the terminal speed please help?? :confused:

Thanks in advance!

Reply 1

brianeverit

9

Original post by firsedge

An object falls through a fluid so that the distance fallen, in metres, at time t seconds is given by s=40(4e^{^(-t/4)} + t - 4). Find the initial and terminal speeds of the object.
I am a bit stuck with the terminal speed please help?? :confused:

Thanks in advance!

Initial speed will be when t=0.
Terminal speed is the limiting value as t tends to infinity.

Reply 2

Flauta

9

Original post by firsedge

An object falls through a fluid so that the distance fallen, in metres, at time t seconds is given by s=40(4e^{^(-t/4)} + t - 4). Find the initial and terminal speeds of the object.
I am a bit stuck with the terminal speed please help?? :confused:

Thanks in advance!

v=\dfrac{ds}{dt}

Find the value of that when t goes to infinity

Reply 3

Plato's Trousers

17

Original post by firsedge

An object falls through a fluid so that the distance fallen, in metres, at time t seconds is given by s=40(4e^{^(-t/4)} + t - 4). Find the initial and terminal speeds of the object.
I am a bit stuck with the terminal speed please help?? :confused:

Thanks in advance!

the speed is the derivative of distance w.r.t. time.

So differentiate the function to get ds/dt (which is speed). Then look at what happens when you let t go to infinity (that's the terminal speed, ie the speed it reaches when time tends to infinity)

Reply 4

firsedge

OP

2

Thats great thanks guys!

Kinematics and variable acceleration question

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