As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of 132 ft / s and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of 7.5 ft / s 2 . (a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes. (b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of 132 ft / s and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of 7.5 ft / s 2 . (a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes. (b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of
132
ft
/
s
and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of
7.5
ft
/
s
2
.
(a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes.
(b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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