Question

a mass of 1000kg having a speed of10m/s is brought to rest overa distance of 100m.find (a) retardation. (b) the retarding force.​

Answer 1

Answer:

• (a) Retardation is 0.5m/s²
• (b) Retarding force is 500N .

Explanation:

According to the Question

It is given that, mass of 1000kg having a speed of 10m/s is brought to rest overa distance of 100m.

Firstly we calculate the retardation.

By using Kinematics Equation

• v² = u² + 2as

by putting the value we get

↠0² = 10² + 2×a × 100

↠ 0 = 100 +200a

↠ -100 = 200a

↠ a = -100/200

↠ a = -0.5m/s²

• Hence, the retardation is 0.5m/s²

Now calculating the retarding force

• F = ma

by putting the value we get

↠ F = 1000 × (-0.5)

↠ F = 100×(-5)

↠ F = -500 N

• Hence, the retarding force is 500 Newton .

Answer 2

Answer:

Given :-

• A mass of 1000 kg having a speed of 10 m/s is brought to rest over a distance of 100 m.

To Find :-

• What is the retardation.
• What is the retardation force.

Formula Used :-

$\clubsuit$ Third Equation Of Motion Formula :

$\longrightarrow \sf\boxed{\bold{\pink{v^2 - u^2 =\: 2as}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• s = Distance Covered

$\clubsuit$ Force Formula :

$\longrightarrow \sf\boxed{\bold{\pink{F =\: ma}}}$

where,

• F = Force
• m = Mass
• a = Acceleration

Solution :-

First we have to find the retardation :

Given :

• Final Velocity = 0 m/s
• Initial Velocity = 10 m/s
• Distance Covered = 100 m

According to the question by using the formula we get,

$\implies \sf (0)^2 - (10)^2 =\: 2a(100)$

$\implies \sf (0 \times 0) - (10 \times 10) =\: 200a$

$\implies \sf 0 - 100 =\: 200a$

$\implies \sf - 100 =\: 200a$

$\implies \sf \dfrac{- 100}{200} =\: a$

$\implies \sf - 0.5 =\: a$

$\implies \sf\bold{\purple{a =\: - 0.5\: m/s^2}}$

Now, we have to find the retardation :-

$\leadsto \bf Retardation =\: - (Acceleration)$

$\leadsto \sf Retardation =\: - (- 0.5)$

$\leadsto \sf\bold{\red{Retardation =\: 0.5\: m/s^2}}$

$\therefore$ The retardation is 0.5 m/s² .

Now, we have to find the retardation force :-

Given :

• Mass = 1000 kg
• Acceleration = 0.5 m/s²

According to the question by using the formula we get,

$\dashrightarrow \sf Force =\: 1000 \times 0.5$

$\dashrightarrow \sf\bold{\red{Force =\: 500\: N}}$

$\therefore$ The retardation force is 500 N .