# Can someone please help me with this calculus physics problem?

The speed of a body released from rest falling through a viscous medium (for instance, an iron pellet falling in a jar full of oil) is given by the formula
v = −g τ + g τ e^( −t /τ )
where τ is a constant that depends on the size and shape of the body and on the viscosity of
the medium and e ≈ 2.718....
(a) Find...
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The speed of a body released from rest falling through a viscous medium (for instance, an iron pellet falling in a jar full of oil) is given by the formula

v = −g τ + g τ e^( −t /τ )

where τ is a constant that depends on the size and shape of the body and on the viscosity of

the medium and e ≈ 2.718....

(a) Find the acceleration as a function of time.

(b) Show that for t → ∞, the speed approaches the terminal value −gτ.

(c) By differentiation, verify that the equation for the position as a function of time consistent with the above expression for the speed is

x=−gτt−gτ^2e−t/τ +gτ^2+x0. (d) What happens for small values of t?

v = −g τ + g τ e^( −t /τ )

where τ is a constant that depends on the size and shape of the body and on the viscosity of

the medium and e ≈ 2.718....

(a) Find the acceleration as a function of time.

(b) Show that for t → ∞, the speed approaches the terminal value −gτ.

(c) By differentiation, verify that the equation for the position as a function of time consistent with the above expression for the speed is

x=−gτt−gτ^2e−t/τ +gτ^2+x0. (d) What happens for small values of t?

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