Question

Figure (i) and (ii) below shows the parabolic displacement time graphs of two particles moving along the x-axis. We can say that

• A. both the particles are speeding up.
• B. both the particles are speeding down.
• C. particle (i) is speeding up while particle (ii) is speeding down.
• D. particle (i) is speeding down while particle (ii) is speeding up.

Answer 1

The correct option is C particle (i) is speeding up while particle (ii) is speeding down.

The slope of displacement - time graph gives the instantaneous velocity. In figure (i), the slope is less in the beginning but it keeps on increasing with time. Thus, velocity of the particle increases with time and hence the particle (i) is speeding up.
In Figure (ii), the slope is more in the beginning and it keeps on decreasing with time. Thus, velocity of the particle decreases with time and hence the particle (ii) is speeding down. The displacement - time graph has convex shape for retarded motion.