Question

A cysliat is moving with a velocity of 10m/s towards east .He suddenly applies brake such tha a retardation of 2m/s²is produced . Calculate how much time Cyclists will take to come into rest​

Answer 1

Answer:

5 seconds is the required answer.

Explanation:

According to the Question

It is given that ,

• Initial velocity ,u = 10m/s
• Final velocity ,v = 0m/s
• Acceleration ,a = -2m/s² (acting in opposite direction)

we need to calculate the time taken by cyclists to come into rest . So we will apply here the kinematics equation.

• v = u + at

where,

v denote final velocity

u denote initial velocity

a denote acceleration

t denote time taken

Substitute the value we get

➻ 0 = 10 + (-2)×t

➻ -10 = -2t

➻ 10 = 2t

➻ 10/2 = t

➻ 5 = t

➻ t = 5s

• Hence, the time taken by the cyclists to come into rest is 5 seconds.

Answer 2

Answer:

Given :-

• A cyclist is moving with a velocity of 10 m/s towards east.
• He suddenly applies brake such the retardation of 2 m/s² is produced.

To Find :-

• How much time cyclist will take to come into rest.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

Solution :-

Given :

$\bigstar\: \: \bf{Final\: Velocity\: (v) =\: 0\: m/s}$

$\bigstar\: \: \bf{Initial\: Velocity\: (u) =\: 10\: m/s}$

$\bigstar\: \: \bf{Acceleration =\: -\: 2\: m/s^2}$

According to the question by using the formula we get,

$\leadsto \bf{v =\: u + at}$

$\longrightarrow \sf (0) =\: (10) + (- 2)(t)$

$\longrightarrow \sf 0 =\: 10 + (- 2) \times t$

$\longrightarrow \sf 0 =\: 10 - 2 \times t$

$\longrightarrow \sf 0 =\: 10 - 2t$

$\longrightarrow \sf 0 - 10 =\: - 2t$

$\longrightarrow \sf {\cancel{-}} 10 =\: {\cancel{-}} 2t$

$\longrightarrow \sf 10 =\: 2t$

$\longrightarrow \sf \dfrac{\cancel{10}}{\cancel{2}} =\: t$

$\longrightarrow \sf \dfrac{5}{1} =\: t$

$\longrightarrow \sf 5 =\: t$

$\longrightarrow \sf\bold{\red{t =\: 5\: seconds}}$

${\small{\bold{\underline{\therefore\: The\: time\: taken\: for\: cyclist\: to\: come\: into\: rest\: is\: 5\: seconds\: .}}}}$

EXTRA INFORMATION :-

❒ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

❒ Second Equation Of Motion Formula :-

$\mapsto \sf\boxed{\bold{\pink{s =\: ut + \dfrac{1}{2}at^2}}}$

❒ Third Equation Of Motion Formula :-

$\mapsto \sf\boxed{\bold{\pink{v^2 =\: u^2 + 2as}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken
• s = Distance Travelled