Question

A body starts from rest and travels with an acceleration of 2 m/s2 if the displacement made by it is 25 m the time to travel t is

Answer 1

Answer:

abody starts from rest and travels for t second with uniform acceleration of 2 m/s². If the displacement made by it is 16 m, what is the time of travel t?

Answer 2

Answer:

Solution :

As per the provided information in the question, we have :

• ✧ Initial velocity (u) = 0 m/s
• ✧ Acceleration (a) = 2 m/s²
• ✧ Displacement (s) = 25 m.

We need to calculate the time raken by body.

Here's the required formula to find the time :

${\longrightarrow{\pmb{\sf{s = ut + \dfrac{1}{2}a{t}^{2}}}}}$

• ✧ s denotes distance/displacement
• ✧ u denotes initial velocity
• ✧ a denotes acceleration
• ✧ t denotes time

Finding the time taken by using second equation of motion :

${\longrightarrow{\sf{s = ut + \dfrac{1}{2}a{t}^{2}}}}$

${\longrightarrow{\sf{25 = (0)(t) + \dfrac{1}{2} \times 2 \times {t}^{2}}}}$

${\longrightarrow{\sf{25 = 0 \times t + \dfrac{1}{2} \times 2 \times {t}^{2}}}}$

${\longrightarrow{\sf{25 = 0 + \dfrac{1}{2} \times 2 \times {t}^{2}}}}$

${\longrightarrow{\sf{25 = 0 + \dfrac{1}{\cancel{2}} \times \cancel{2} \times {t}^{2}}}}$

${\longrightarrow{\sf{25 = 0 + 1 \times {t}^{2}}}}$

${\longrightarrow{\sf{25 - 0 = 1 \times {t}^{2}}}}$

${\longrightarrow{\sf{25 = {t}^{2}}}}$

${\longrightarrow{\sf{{t}^{2} = 25}}}$

${\longrightarrow{\sf{t = \sqrt{25} }}}$

${\longrightarrow{\sf{t = \sqrt{5 \times 5} }}}$

${\longrightarrow{\sf{\underline{ \underline{\red{t =5 \: sec}}}}}}$

Henceforth, the time travel is 5 second.

Learn More :

• ✧ Velocity

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{v = u + at}}}}}}}$

• ✧ Displacement with positive accelerations

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{s= ut + \dfrac{1}{2}{at}^{2}}}}}}}}$

• ✧ Displacement with negative acceleration

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{s= ut - \dfrac{1}{2}{at}^{2}}}}}}}}$

• ✧ Displacement knowing initial and final speeds

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{s= \dfrac{1}{2}\big(u + v \big)t}}}}}}}$

• ✧ Velocity squared

${\longrightarrow{\small{\underline{\boxed{\sf{\purple{{v}^{2} = {u}^{2} + 2as}}}}}}}$

$\underline{\rule{220pt}{4pt}}$