A force F acting on a body of mass m a distance r from some origin has magnitude F = Ame^-r/r⁴, where A and are both constants. The constant e = 2.718... Given that the force has dimensions kilogram meter per seconds squared, what are the dimensions of the following? (Use M, L and T as necessary.)

(a) the constant

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1
(b) the constant A

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2

The velocity of an object moving in a viscous fluid is given by the following expression, where t is measured in seconds.

v(t) = (5.6 m/s) + (7.9 m/s)e^-0.5t

Calculate the acceleration of the object as a function of time t.

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1
Using this result and the expression for v(t), write the acceleration as a function of the velocity v.

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2

The position of a particle in a given coordinate system is r(t) = (3 - 2t²) i + (-2 + 2t) j where the distances are in meters when t is in seconds. At what time will the particle cross the y-axis?

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1 s
At what time will it cross the x-axis?

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2 s
Find an equation that relates the y-coordinate to the x-coordinate and therefore gives the trajectory in the xy-plane. (Answer in terms of y.)
x =

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3
Where would the x- and y-axes have to be moved so that at t = 0 s the trajectory passes through the origin?
x =

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4
y =

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5

A skater is gliding at what is very close to constant speed on a frozen lake. (There is negligible friction between blade and ice.) A stiff but very steady wind is blowing. What are the forces acting on the skater? (Select all that apply.)

Do they balance?
Explain.
3

A large laser designed for nuclear fusion can produce 5.5 10⁴ J of energy over a time period of 0.6 10^-9 s.

(a) How much power can such a laser produce during its discharge?

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1 kW
(b) How much power is required to reenergize it over a period of 23 min?

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2 W