Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
A particle starts moving from rest from a fixed point in a fixed direction. The
A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time \( t \) is given by \( s=t^{2}+a t-b+17, \) where \( a \) and \( b \) are real numbers. If the particle comes to rest after \( 5 s \) at a distance of \( s=25 \) units from the fixed point, then value of \( a \) and \( b \) are respectively.
- A. 10,-33
- B. -10,-33
- C. -8,33
- D. -10,33
Step-by-step solution
Given s=t^2+at-b+17, velocity v=ds/dt=2t+a. Particle comes to rest at t=5, so v(5)=0 => 10+a=0 => a=-10. Also s(5)=25 => 25+(-10)*5-b+17=25 => -8-b=25 => b=-33. Thus a=-10, b=-33, matching option B. The phrase 'starts from rest' is additional but not needed for solution.
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