A particle moving along a straight track experiences an acceleration that varies with…
PHYSICS · Multi-part · CBSE · Physics · Motion in a Straight Line · Motion in a Straight Line
Problem
A particle moving along a straight track experiences an acceleration a(t) that varies with time as follows.
• For 0≤t≤2 s, the acceleration is constant at 3 m/s2.
• For 2<t≤5 s, the acceleration is zero.
• For 5<t≤8 s, the acceleration is constant at −2 m/s2.
At t=0 the particle is at position x=0 with velocity v=4 m/s. No other forces act on the particle.
(a) Without performing detailed calculations, describe the intervals of time during which the particle’s velocity is increasing, constant, or decreasing. Justify your answer in terms of the sign and magnitude of the acceleration.
(b) Explain how the concavity of the position–time graph changes over the three time intervals. State your reasoning clearly in terms of acceleration.
(c) The particle’s displacement on each of the three intervals is denoted by Δx1, Δx2, and Δx3, respectively. Without computing exact numerical values, rank ∣Δx1∣, ∣Δx2∣, and ∣Δx3∣ from greatest to least, providing a brief justification for your ranking.
(d) Determine whether the particle can return to its starting position (x=0) during the interval 0≤t≤8 s. Support your conclusion with a qualitative argument based on the given information.