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2.Motion in Straight Line
normal
An object at rest at the origin begins to move in the $+x$-direction with a uniform acceleration of $1 \,m / s ^2$ for $4 \,s$ and then it continues moving with a uniform velocity of $4 \,m / s$ in the same direction.The $x-t$ graph for object's motion will be
A
B
C
D
(KVPY-2015)
Solution
(b)
Initially, the velocity is increasing, so the $(x-t)$ graph must be with increasing slope or parabolic.
For first $4-s$, $x=u t+\frac{1}{2} a t^2$
$\Rightarrow \quad x=t^2 / 2$ (parabola).
After $4 \,s$, particle is moving with a constant velocity, so its graph is a straight line of constant slope after $4 \,s$. After $4 \,s$, velocity is constant.
$\therefore x=v t=(4+a t) t=4 t$ (straight line)
Hence, best suited option is $(b)$.
Standard 11
Physics
