A constant retarding force of $50\ \text{N}$ is applied to a body of mass $20\ \text{kg}$ moving initially with a speed of $15\ \text{m s}^{-1}$. How long does the body take to stop?

> [!TLDR] > The retarding force causes a constant deceleration, which can be used with the initial velocity to find the time taken to stop. The body takes $\boxed{6\ \text{s}}$ to stop. Let's understand what's happening here. We have a body moving with a certain initial speed, and a constant force is applied in the opposite direction to its motion. This force is called a retarding force because it tries to slow the body down. Eventually, if the force acts long enough, the body will come to a complete stop. We need to find out how much time this process takes. The core idea here is to relate the force to the change in motion. Newton's second law of motion directly connects force, mass, and acceleration. Once we find the acceleration (or rather, deceleration, since it's a retarding force), we can use the equations of motion to find the time. 1. **Determine the acceleration:** A constant retarding force means the body experiences a constant acceleration in the direction opposite to its initial velocity. We can find this acceleration using Newton's second law: $F = ma$. Here, $F = 50\ \text{N}$ (the magnitude of the retarding force) and $m = 20\ \text{kg}$. The acceleration $a$ will be: $$a = \frac{F}{m}$$ $$a = \frac{50\ \text{N}}{20\ \text{kg}}$$ $$a = 2.5\ \text{m s}^{-2}$$ Since this is a retarding force, the acceleration is in the opposite direction to the initial velocity. So, we can consider it as a deceleration, meaning its value will be negative if we take the initial velocity direction as positive. 2. **Identify the known kinematic variables:** We are given: * Initial velocity, $u = 15\ \text{m s}^{-1}$ (let's take this direction as positive). * Final velocity, $v = 0\ \text{m s}^{-1}$ (since the body stops). * Acceleration, $a = -2.5\ \text{m s}^{-2}$ (negative because it's a deceleration). * We need to find the time, $t$. 3. **Apply the appropriate equation of motion:** …

A constant retarding force of 50N is applied to a body of mass 20kg moving initially with a speed of 15m s⁻¹.

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50\ \text{N}

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Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.

The Intuition First

Two things matter when you push something:

How hard you push — the force you apply.
How heavy the object is — its mass.

The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.

Note

"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."

The Precise Statement

Newton's Second Law says:

The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.

In one equation:

\vec{a} = \frac{\vec{F}_{\text{net}}}{m}

Or more commonly:

\vec{F}_{\text{net}} = m \vec{a}

Where:

$\vec{F}_{\text{net}}$ is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
$m$ is the mass of the object — measured in kilograms (kg)
$\vec{a}$ is the acceleration — measured in metres per second squared ( $\text{m/s}^2$ )

\vec{F}_{\text{net}} = m \vec{a}

What This Really Means

Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).

Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.

Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.

A Simple Example

A 2 kg block is pushed with a net force of 10 N to the right.

a = \frac{F_{\text{net}}}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2

The block accelerates at $5\ \text{m/s}^2$ to the right. Every second, its velocity increases by 5 m/s in that direction. …

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The retarding force causes a constant deceleration, which can be used with the initial velocity to find the time taken to stop. The body takes $\boxed{6\ \text{s}}$ to stop.

Let's understand what's happening here. We have a body moving with a certain initial speed, and a constant force is applied in the opposite direction to its motion. This force is called a retarding force because it tries to slow the body down. Eventually, if the force acts long enough, the body will come to a complete stop. We need to find out how much time this process takes.

The core idea here is to relate the force to the change in motion. Newton's second law of motion directly connects force, mass, and acceleration. Once we find the acceleration (or rather, deceleration, since it's a retarding force), we can use the equations of motion to find the time.

Determine the acceleration: A constant retarding force means the body experiences a constant acceleration in the direction opposite to its initial velocity. We can find this acceleration using Newton's second law: $F = ma$ . Here, $F = 50\ \text{N}$ (the magnitude of the retarding force) and $m = 20\ \text{kg}$ . The acceleration $a$ will be:

a = \frac{F}{m}

a = \frac{50\ \text{N}}{20\ \text{kg}}

a = 2.5\ \text{m s}^{-2}

Since this is a retarding force, the acceleration is in the opposite direction to the initial velocity. So, we can consider it as a deceleration, meaning its value will be negative if we take the initial velocity direction as positive.

2. Identify the known kinematic variables:

We are given:

* Initial velocity, $u = 15\ \text{m s}^{-1}$ (let's take this direction as positive).

* Final velocity, $v = 0\ \text{m s}^{-1}$ (since the body stops).

* Acceleration, $a = -2.5\ \text{m s}^{-2}$ (negative because it's a deceleration).

* We need to find the time, $t$ .

Apply the appropriate equation of motion: …

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Q.A constant retarding force of $50\ \text{N}$ is applied to a body of mass $20\ \text{kg}$ moving initially with a speed of $15\ \text{m s}^{-1}$ . How long does the body take to stop?

Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

The Intuition First

The Precise Statement

What This Really Means

A Simple Example

Concept: Newton's Second Law + Equations of Motion (kinematics)

Q.A constant retarding force of 50 N50\ \text{N}50 N is applied to a body of mass 20 kg20\ \text{kg}20 kg moving initially with a speed of 15 m s−115\ \text{m s}^{-1}15 m s−1. How long does the body take to stop?

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Q.A constant retarding force of $50\ \text{N}$ is applied to a body of mass $20\ \text{kg}$ moving initially with a speed of $15\ \text{m s}^{-1}$ . How long does the body take to stop?

Unlock everything free for 14 days