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A motorcyclist heading east through a small town accelerates at a constant 4.0m/s² after he leaves the city limits. at time t=0 he is 5.0 m east of the city-limits signpost, moving east at 15m/s; find his position and velocity at t=2.0s

User Harish ST
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Final answer:

To find the position and velocity of the motorcyclist at t=2.0 s, we use the kinematic equations for constant acceleration. The final velocity is 23 m/s, and the total distance from the start is 43 m east.

Step-by-step explanation:

The student is asking to find the position and velocity of a motorcyclist who accelerates at a constant acceleration from a given initial velocity and position. The motorcyclist starts 5 meters east of the city-limits signpost with an initial velocity of 15 m/s, and accelerates at 4.0 m/s2 eastward.

To determine the motorcyclist's position and velocity at t=2.0 s, we can use the kinematic equations for uniformly accelerated motion.

The final velocity (v) can be found using the equation:
v = u + at
Where u is the initial velocity, a is the acceleration, and t is the time. Thus, we get:

v = 15 m/s + (4.0 m/s2)(2.0 s) = 23 m/s

The position (s) can be found using the equation:
s = ut + 1/2 at2
Where s is the displacement from the starting point. Hence:

s = (15 m/s)(2.0 s) + 1/2 (4.0 m/s2)(2.0 s)2 = 30 m + 8 m = 38 m

The final position of the motorcyclist at t=2.0 s is 5.0 m + 38 m = 43 m east of the city-limits signpost.

User Avinash Garg
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