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A Force F = α + B X Acts on a Particle in the X-direction, Where a and B Are Constants. Find the Work Done by this Force During a Displacement from X = 0 to X = D. - Physics

Sum

A force \[F = \alpha + bx\]  acts on a particle in the x-direction, where a and b are constants. Find the work done by this force during a displacement from x = 0 to x = d. 

 
 
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Solution

Given that force is a function of displacement, i.e.

\[F = a + bx\] ,
where a and b are constants.
So, work done by this force during the displacement x = 0 to x = d,
\[W = \int\limits_0^d F \text{ dx } \]
\[W = \int\limits_0^d \left( a + bx \right) dx\]
\[W = \left[ ax + \frac{b x^2}{2} \right]_0^d \]
\[W = ad + \frac{b d^2}{2}\]
\[ \Rightarrow W = \left( a + \frac{bd}{2} \right)d\] 
  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 8 Work and Energy
Q 8 | Page 133
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