Question

A constant retarding force of 50N is applied to a body of body 20kg moving with a speed of 15m/s .How long does the body take to stop?

Answer 1

In F = ma , where F is the resultant force, the force that is against the direction of the object's current velocity is the retarding force. For example, for a car, its forward force is F from motor.

Answer 2

Given:

Retarding force (F) = -50 N

Mass of body (m) = 20 kg

Initial speed (u) = 15 m/s

Final speed (v) = 0 m/s (Stop)

To Find:

Time taken by body to stop (t)

Answer:

★ Force is the product of mass (m) and accelration (a) of the body.

$\boxed{ \boxed{ \bf{F = ma}}}$

By substituting values we get:

$\rm \implies - 50 = 20 a \\ \\ \rm \implies a = - \dfrac{5 \cancel{0}}{2 \cancel{0}} \\ \\ \rm \implies a = - 2.5 \: m {s}^{ - 2}$

• Negative sign of acceleration denotes the retarding motion of the body.

Retardation (a) = -2.5 m/s²

★ From $\sf 1^{st}$ Equation of motion we have:

$\boxed{ \boxed{ \bf{v = u + at}}}$

By substituting values we get:

$\rm \implies 0 = 15 + ( - 2.5)t \\ \\ \rm \implies 2.5t = 15 \\ \\ \rm \implies t = \dfrac{15}{2.5} \\ \\ \rm \implies t = 6 \: s$

$\therefore$ $\boxed{\mathfrak{Time \ taken \ by \ body \ to \ stop \ (t) = 6 \ s}}$