A) The position at t = 2.0 sec is 43.0 m east
B) The position is 55 m east
Explanation:
A)
In order to solve the problem, we take the east direction as positive direction.
We know that:
- at t = 0, the motorcyclist is at a position of 
- at t = 0, the initial velocity of the motorcyclist is
east
- The acceleration of the motorcyclist is constant and it is 
Since the motion is a uniformly accelerated motion, the position of the motorcylist is given by the expression

where t is the time.
Substituting t = 2.0 s, we find the position:

B)
The velocity of the motoryclist can be found by calculating the derivative of the position. Therefore, it is:

where:
is the initial velocity
is the acceleration
We want to find the time t at which the velocity is
v = 25 m/s
Solving the equation for t,

And therefore, the position at t = 2.5 s is:

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