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Let and represent the velocity and acceleration, respectively, of an automobile. Describe circumstances in which (a) and are parallel; (b) and © are perpendicular to one another; (d) is not zero; (e)

Let  and represent the velocity and acceleration, respectively, of an automobile. Describe circumstances in which (a)  and  are parallel; (b)  and  © are perpendicular to one another; (d)   is not zero; (e)

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
7 years ago
(a) Consider a situation in which the automobile heads on a straight road, accelerating uniformly and increasing its speed. The acceleration vector and the velocity vector of the automobile both point in the same direction and are parallel to each other.
(b) Consider a situation in which the driver of an automobile, initially moving with constant velocity, applies the brake such that the automobile start decelerating. The acceleration vector of the automobile is in the direction opposite to the motion of vehicle and its velocity vector.Therefore the acceleration vector and the velocity vector are antiparallel to each other.
(c) Consider an automobile moving in uniform circular motion about a reference point. The direction of the velocity vector is tangential to the path traced by the automobile while the acceleration is always perpendicular to the velocity vector, directed towards the reference point.
(d) Consider a car moving up the hill with a larger angle of inclination. The car cannot make it to the top of the hill even with full engine power and is expected come back to the bottom under the action of gravity. At the maximum attainable height, the car comes momentarily at rest, and therefore has zero velocity However, the gravitational force pulls on the car to accelerate it in the direction of the slope.Therefore, the automobile has zero velocity but non-zero acceleration at that point.

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