A particle of mass moves on the -axis as follows : it starts from rest at from the point
MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics
Problem
A particle of mass m moves on the x-axis as follows : it starts from rest at t=0 from the point x=0 , and comes to rest at t=1 at the point x=1 . NO other information is available about its motion at intermediate times ( 0<t<1 ). If α denotes the instantaneous acceleration of the particle, then:
(1) α cannot remain positive for all t in the interval 0≤t≤1 .
(2) ∣α∣ cannot exceed 2 at any point in its path.
(3) ∣α∣ must be ≥4 at some point or points in its path.
(4) α must change sign during the motion, but no other assertion can be made with the information given.