WBJEE · Maths · Differentiation
The law of motion of a body moving along a straight line is \(x=\frac{1}{2}\) vt. \(x\) being its distance from a fixed point on the line at time \(t\) and \(v\) is its velocity there, Then
- A acceleration \(f\) varies directly with \(x\)
- B acceleration \(f\) vares inversely with \(x\)
- C acceleration \(f\) is constant
- D acceleration \(f\) varies directly with t
Answer & Solution
Correct Answer
(C) acceleration \(f\) is constant
Step-by-step Solution
Detailed explanation
We have, \(\quad x=\frac{1}{2} v t\) \(\Rightarrow \quad x=\frac{1}{2} \frac{d x}{d t} t\) \(\left[\because v=\frac{d x}{d t}\right]\) \(\Rightarrow \quad \frac{2 d t}{t}=\frac{d x}{x}\) \(\Rightarrow \quad 2 \cdot \int \frac{d t}{t}=\int \frac{d x}{x}\)…
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