Question

Figure (i) and (ii) below show the 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 velocity. In figure (i), the slope is low in the beginning but it keeps on increasing with time. Thus, velocity of the particle increases with time and hence the particle (i) has accelerated motion. The displacement –time graph has concave shape for accelerated motion.
In Figure (ii), the slope is high in the beginning and it keeps on decreasing with time. Thus, velocity of the particle decreases with time and hence the particle (ii) has retarded motion. The displacement – time graph has convex shape for retarded motion.
For uniformly accelerated or retarded motion, the shape of displacement –time graph is parabolic (which look to be true for given graphs).