A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement-time graph is characterized by:

Question

A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement-time graph is characterized by: (A) negative slope and zero curvature (B) zero slope and negative curvature (C) zero slope and positive curvature (D) positive slope and zero curvature

Tardigrade Admin · Accepted Answer

At the highest point of projectile motion, the tangent drawn is parallel to x-axis. Hence, slope at this point is zero. Moreover, the curve is convex upwards, hence curvature is positive at this point.

Q. A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement-time graph is characterized by:

negative slope and zero curvature

zero slope and negative curvature

zero slope and positive curvature

positive slope and zero curvature

At the highest point of projectile motion, the tangent drawn is parallel to x-axis. Hence, slope at this point is zero. Moreover, the curve is convex upwards, hence curvature is positive at this point.