Question

Displacement vs. time graph of a body projected vertically up is:

• A. a straight line
• B. a parabola
• C. a hyperbola
• D. a circle

Answer 1

Answer: (B)

a parabola

Since the body is projected vertically upwards, there is no force/velocity along $x$ axis. On the $y$ axis, gravitational force is acting on the particle.
Using second equation of motion, displacement along $y$ axis, i.e. $s$, is given by:
Also, $s=ut-\left(\frac{1}{2}\right)g{t}^2$
Thus, between, $s$ and $t$, the above equation is an equation of parabola between $s$ and $t$.
This is the equation of a parabola which is symmetric about the $y-$axis.Thus,the path of projectile,projected vertically above the ground is a parabola.
For example, in the attached graph, you can see the graph of displacement vs time of a body thrown up with an initial velocity of $50m/s$.