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

Correct answer: (B). V=0+1 × t (d x)/(d t)=t d x=t dt x ∝ t^2 … … … Parabolic (d x)/(d t)=4 d x=4 d t x ∝ t … … … Linear

Q41 / 60 · KVPY 2015 (SA) · Physics

An object at rest at the origin begins to move in the $+x$ direction with a uniform acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$ for $4 \mathrm{~s}$ and then it continues moving with a uniform velocity of $4 \mathrm{~m} / \mathrm{s}$ in the same direction. The $\mathrm{x}-\mathrm{t}$ graph for object's motion will be

A
Correct answer
B
C
D

Solution

$$ \begin{array}{l} \mathrm{V}=0+1 \times \mathrm{t} \\ \frac{d x}{d t}=t \\ d x=t \mathrm{dt} \\ x \propto t^{2} \quad \ldots \ldots \ldots \\ Parabolic \frac{d x}{d t}=4 \\ d x=4 d t \\ x \propto t \quad \ldots \ldots \ldots Linear \end{array} $$

Hence, the correct answer is option: 'B'.

Solution

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