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A body starts from rest and travels fort
second with uniform acceleration of 2 m/s2
If the displacement made by it is 16 m, the
time of travel tis
Select one:​

Answer 1

Explanation:

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

• Initial velocity (u) = 0 m/s (As it starts from rest)
• Acceleration (a) = 2 m/s²
• Displacement (s) = 16 m

We are asked to calculate the time taken (t seconds).

Here, we can use one of the three equations of motion to find the time taken. Mainly, there are three equations of motion :

$\boxed{ \begin{array}{cc} \pmb{\sf{ \quad \: v = u + at \quad}} \\ \\ \pmb{\sf{ \quad \: s= ut + \cfrac{1}{2}a{t}^{2} \quad \: } } \\ \\ \pmb{\sf{ \quad \: {v}^{2} - {u}^{2} = 2as \quad \:}}\end{array}}$

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

Here, we have s, a and u. So, we can apply the 2nd equation of motion to find the time taken.

By using the second equation of motion,

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

Substituting the values we have.

$\longrightarrow \sf { 16 = (0 \times t) + \dfrac{1}{2} \times 2 \times t^2 }$

$\longrightarrow \sf { 16 = \dfrac{1}{2} \times 2 \times t^2 }$

$\longrightarrow \sf { 16 = 1 \times 1 \times t^2 }$

$\longrightarrow \sf { 16 = t^2 }$

$\longrightarrow \sf {\sqrt{ 16 }= t }$

$\sf \red { \longrightarrow { 4 = t }}$

∴ The time travel of it is 4 seconds.