Question

A sledge starts from rest and accelerates at 1.5m/s^2 until velocity is 2.8m/s
a)show that time taken to reach 2.8 m/s is about 2s
pls tell with steps​

Answer 1

Answer :-

Given :-

• Initial velocity = 0 m/s
• Final velocity = 2.8 m/s
• Acceleration = 1.5 m/s²

To find :-

• Time taken

Solution :-

• u = 0 m/s
• v = 2.8 m/s
• a = 1.5 m/s²

Substituting the values in 1st equation of motion :-

➱ $\boxed{\rm v = u + at}$

➱ $\rm 2.8 = 0 + 1.5t$

➱ $\rm 2.8 = 1.5t$

➱ $\rm t = \dfrac{2.8}{1.5}$

➱ $\boxed{\rm t = 2} \: \sf( approx )$

Hence, the time taken to reach velocity of 2.8 m/s is 2 seconds.

Answer 2

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{Initial\: velocity\:(u) = 0 \:m/s }$

$\:\:\:\:\bullet\:\:\:\sf{Final \ velocity \: (v) = 2.8 \ m/s }$

$\:\:\:\:\bullet\:\:\:\sf{Acceleration \: (a) = 1.5 \ m/s^{2}}$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{Time \ taken \ (t) = \:? }$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

☯ Using 1st equation of motion :-

$\dashrightarrow\:\: \sf{ v = u + at}$

$\dashrightarrow\:\: \sf{ 2.8 = 0 + 1.5t}$

$\dashrightarrow\:\: \sf{ 2.8 = 1.5t}$

$\dashrightarrow\:\: \sf{ t = \dfrac{2.8}{1.5}}$

$\dashrightarrow\:\: \sf{t = 1.8\overline{6}}$

$\dashrightarrow\:\: \sf{ t = 2 \:(approximately)}$

Hence,

• Time taken to reach velocity of 2.8 m/s is $\bf{2\: seconds}$

${\mathfrak{\underline{\purple{\:\:\:Additional \:Information:-\:\:\:}}}}$

$\star\:\sf{Some\:equation\: of \:motion }$

$\boxed{</p><p></p><p>\begin{minipage}{3 cm} \\</p><p></p><p>\sf{\:\bullet\:\:v = u +at} \\ \\</p><p></p><p>\sf{\:\bullet\:\:s = ut + \frac{1}{2}\:at^{2} }\\ \\</p><p></p><p>\sf{\:\bullet\:\:v^{2} = u^{2} + 2as}\\ \\</p><p>\sf{\:\bullet\:\:s = \dfrac{1}{2} (u + v)t}\\ </p><p></p><p>\end{minipage}</p><p></p><p>}$

$\sf{Where,}$

$\:\:\:\:\bullet\:\:\:\textsf{v = Final velocity}$

$\:\:\:\:\bullet\:\:\:\textsf{u = Initial velocity}$

$\:\:\:\:\bullet\:\:\:\textsf{a = Acceleration}$

$\:\:\:\:\bullet\:\:\:\textsf{s = Distance}$

$\:\:\:\:\bullet\:\:\:\textsf{t = Time taken}$