Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":

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**(a)**

For constant speed:

Δx = ct

x_{final} - x_{initial} = ct

x_{final} = x_{initial} + ct

x_{final} = x_{man}

Assuming the bus is moving in a positive direction, x_{initial} = -b

A man is running at speed *c* (much less than the speed of light) to catch a bus already at a stop. At *t *= 0, when he is a distance *b* from the door to the bus, the bus starts moving with the positive acceleration *a*. Use a coordinate system with *x *= 0 at the door of the stopped bus.

a) What is *x*_{man}(*t*), the position of the man as a function of time? Answer symbolically in terms of the variables *b*, *c*, and *t*.

b) What is *x*_{bus}(*t*), the position of the bus as a function of time? Answer symbolically in terms of *a* and *t*.

c) What condition is necessary for the man to catch the bus? Assume he catches it at time *t*_{catch}.

a. *x*_{man}(*t*_{catch}) > *x*_{bus}(*t*_{catch})

b. *x*_{man}(*t*_{catch}) = *x*_{bus}(*t*_{catch})

c. *x*_{man}(*t*_{catch}) < *x*_{bus}(*t*_{catch})

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