Question

A particle moves with uniform acceleration 0.5m/s2 in a horizontal line ABC. The speed of the particle at C is 80m/s and the times taken from A to B and from B to C are 40 and 30 seconds respectively. Calculate (a) Speed at A (b) Distance BC

Answer 1

$\huge\mathbb\color{pink}\underline{\underline{\dag{Question:}}}$

$\textsf{A particle moves with uniform acceleration 0.5}$$\textsf{m/s² in a horizontal line ABC . The speed of the}$$\textsf{particle at C is 80m/s and the time taken from}$$\textsf{A to B from B to C are 40 and 30 seconds}$$\textsf{respectively. Calculate (a) Speed at A (b)}$$\textsf{Distance BC}$

$\huge\mathbb\color{green}\underline{\underline{\dag{Given:}}}$

$\textsf{Uniform acceleration horizontal lineABC=0.5m/s²}$

$\textsf{Speed of partical at C = 80m/s}$

$\textsf{Time taken from A to B = 40 seconds}$

$\textsf{Time taken from B to C = 30 seconds}$

$\huge\mathbb\color{Brown}\underline{\underline{\dag{To\:find:}}}$

$\textsf{(a) Speed at A}$

$\textsf{(b) Distance from B to C}$

$\huge\mathbb\color{cyan}\underline{\underline{\dag{Taken:}}}$

$\bold\purple{S=T×U}$

$\bold{Where,}$

$\bold{S=Speed\:at\:A}$

$\bold{T=Time\:taken\:to\:travel\:the\:distance}$

$\bold{U=Uniform\:Acceleration}$

$\bold\purple{D=S×T}$

$\bold{Where,}$

$\bold{D=Distance}$

$\bold{S=Speed}$

$\bold{T=Time\:taken}$

$\huge\mathbb\color{blue}\underline{\underline{\dag{Concept:}}}$

$\textsf{Find the speed from A to B then find the}$$\textsf{distance from B to C}$

$\huge\mathbb\color{magenta}\underline{\underline{\dag{Solution:}}}$

(a)Speed at A

$\bold\purple{Taken,S=T×U}$

$\bold{S=40s×0.5m/s²}$

$\bold{S=20m/s}$

_____________________________________

(b) Distance from B to C

$\bold\purple{Taken,D=S×T}$

$\bold{First,find\:the\:speed\:from\:B\:to\:C}$

$\bold{Using\:this\:formula,S=T×U}$

$\bold{S=30s×0.5m/s²}$

$\bold{S=15m/s}$

$\bold{Now,find\:the\:distance}$

$\bold{D=S×T}$

$\bold{D=15m/s×30s}$

$\bold{D=450m}$

Answer:

(a) Speed at A = 20 m/s

(b) Distance from B to C = 450 m

____________________________________

$\huge\mathbb\color{red}\underline{\underline{\dag{Extra\:information}}}$

$\bold{• Acceleration = \frac{Final\:velocity-Initial\:velocity}{Time}}$

$\bold{• Time = \frac{Distance}{Speed}}$

HOPE IT HELPS YOU