How to Calculate Speed from Force and Mass: Several Approaches and Problem Examples

The article discusses about several approaches of how to calculate speed from force and mass along with its solved problems. 

To calculate speed, we must understand how far an object has mass gone when force is applied. The object’s speed is nothing but a magnitude of its velocity vector. That’s why we can calculate speed from force and mass by using Newton’s Laws, Kinematics Equation of Motion and Work-Energy Formulas.

Read more about How to calculate Mass from Force and Distance.

How to Calculate Speed from Force and Mass using Newton’s Second Law?

Let’s calculate speed from force and mass employing Newton’s second law of motion. 

Newton’s second law connects the rate of velocity change or acceleration with applied force and mass. To calculate speed from Newton’s second law, we first need to understand the difference between speed and velocity and then calculate the speed value from the rate of velocity change. 

As per Newton’s second law,

F=ma

]

F=m*[(v-v0)/(t-t0)

Whereas v0 is the initial velocity and v is the final velocity

Before calculating speed using Newton’s law, let’s comprehend the differences between speed and velocity.

How to Calculate Speed from Force and Mass
How to Calculate Speed
from Force and Mass

Difference between Speed and Velocity

SpeedVelocity
It is a scalar quantity related to distance.It is a vector quantity related to displacement.
It is the non-zero quantity that is always positive.It can be zero, positive and negative.
It may not be equal to velocity.The different velocities of the same object possess equal speed.
SI unit is meter/second (m/sec).SI unit is kilometre/hour (km/hr).
Speed Vs Velocity
(credit: shutterstock)

When the car travelled with a certain distance d over time t, we call its speed v.

v=d/t

As you know, sometimes we need to change our direction while driving due to traffic or other reasons; in that case, we measure the displacement instead of distance d in time interval t.

The equation (*) becomes the velocity v as,

Displacement is the shortest distance between final and initial distance, but its magnitude is less than or equal to the total distance d. 

How to Calculate Speed from Distance
Distance Vs Displacement
(credit: shutterstock)

Since speed is nonzero or never decreases with time, the velocity magnitude becomes the speed value when the time approaches zero. 

That means speed v tells us how fast the car is. Whereas velocity v tells us both how fast the car is and its direction. Therefore, we called speed as the magnitude of the velocity vector

Read more about Relative Motion.

The car has a mass of 1000 kg at rest travelled about 1 hour when a force of 6 x 104 N is applied. Calculate the speed of the car.

Given:

F= 6 x 104 N

m= 1000 kg

t= 1 hour

To Find: v=?

Formula:

F=ma

Solution:

The speed of the car is calculated using Newton’s second law of motion.

F = ma

F=m*[(v-v0)/(t-t0)

Since the car initially at rest, v0 = 0 and t0 = 0

Therefore,

Substituting all values,

Let’s convert the velocity into speed in metre per second.

1km = 1000m

1hour= 3600sec

v=60*(1000/3600)

v=60000/3600

v = 16.6

The car moves with speed 16.6 m/sec.

Read more about How to Calculate Gravitational Acceleration.

How to Calculate Speed from Force and Mass using Kinematics Equation of Motion?

Let’s calculate speed from force and mass using the second kinematics equation of motion. 

The second kinematics equation of motion links the object’s total distance travelled to the initial velocity and acceleration. When we implemented the acceleration formula from Newton’s second law into the kinematics equation, we acquired a formula that calculated the speed from applied force and its mass. 

The second kinematics equation of motion is,

How to calculate Speed from Force and Mass using Kinematics Equation
How to calculate Speed from Force and Mass using Kinematics Equation

Read more about Kinematics Equations of Motion.

A skydiver with a mass of 60 kg jumps from the plane and reaches the ground in 1 minute. If the force entered by air on the skydiver is 800 N, what is the skydiver’s speed?

Given:

m = 60 kg

t = 1 minutes = 60 secs

F = 800 N

To Find: v=?

Formula:

Solution:

The speed of the skydiver is calculated using the second kinematics equation of motion.

a=F/m

But

Since the skydiver is initially at rest with respect to the plane, hence, d0 = 0 and v0 = 0.

d=(1/2)*(F/m)*t2

Since speed v= d/t

vt=(1/2)*(F/m)*t2

v=Ft/2m

Substituting all values

v=(800*60)/(2*60)

v=48000/120

V= 400

The speed of a skydiver is 400 m/sec.

Read more about Potential to Kinetic Energy Conversion.

How to Calculate Speed from Force and Mass using Work-Energy Formula?

Let’s calculate speed from force and mass using the work-energy formula. 

When an object at rest travels a certain distance when force is applied, it performs work. The applied force converts the stored potential energy of the stationary object to kinetic energy to perform work. That’s why using the work-energy formula; we can calculate speed from force and mass. 

The work formula is,

W= Fd

Since work done of an object is its gaining in kinetic energy KE=(1/2)mv2

(1/2)mv2 =Fd

Read more about Work Done.

The man has mass 80 kg slides with 30km/hr in 2 secs when the force of 200N applies on him by pushing on a playground slide. Calculate the speed of man sliding. 

Given:

F= 200 N

m= 80 kg

v=30km/hr=30*(1000/3600)

t= 2 hr

To Find: v=?

Formula:

(1/2)mv2=Fd

Solution:

The speed of sliding of man is calculated using work-energy formula as,

(1/2)mv2=Fd

But speed v = d/t

(1/2)mv2=Fdt

v=mv2/2Ft

Using the work-energy formula, we can calculate the speed in terms of force, mass and velocity.

Substituting all values,

v=(72*106)/(28.8*105)

v = 25

The speed of sliding of man is 25 m/sec.

Read more about Work done on Incline.

How to Calculate Speed from Force and Mass using Power Formula?

Let’s calculate speed from force and mass using the power Formula. 

The power of any object is measured as the amount of its work done in unit time. Since the object’s work done is the product of applied force, and its distance travelled. Therefore, using the power formula, we can calculate the object’s speed directly from the applied force and its power.  

The power formula is,

P=W/t

W=Fd

But workdone

P=Fd/t

v=d/t

Since speed

P=Fv

How to calculate Speed from Force and Mass using Power Formula
How to calculate Speed from Force and Mass using Power Formula
(credit: shutterstock)

Read more about Power

If the motor’s power rating is 500 W, that can do work done when the force of 80 N applies. What is the speed of the motor?

Given:

P= 500 W

1W=1kg.m2/s3

F=80 N

1N=1kg.m2/s2

To Find: v=?

Formula:

P=W/t

Solution:

The speed is calculated using the power formula,

P=Fv

v=P/F

Substituting all values,

V=500W/80N

v = 40 m/sec

The speed of the motor is 40m/sec.


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