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Elvis is in a speeding car moving in the trajectory x(t) = (40 m/s)t along the...

Elvis is in a speeding car moving in the trajectory x(t) = (40 m/s)t along the x axis and t is the time in seconds. An Elvis fan is moving in the trajectory x(t) = −400 m − (20 m/s)t + (4 m/s^2 )t^2 .

Sketch the initial positions of Elvis and the fan’s car in an appropriate coordinate system.

Find the time at which the fan’s car has zero instantaneous velocity, v(t) = 0.

Find when Elvis and the fan’s car have the same velocity.

Find the time when the fan catches up with Elvis.

Find how far, in feet, Elvis has moved when the fan catches up to him. Assume 1 m = 3 ft

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