Laws Of Motion

The velocity-time graphs are given below:

i. Distance refers to "how much length an object has covered" during its motion. And, displacement refers to "how far out of place an object is"; It is the object's overall change in position.

ii. It depends only on magnitude not on direction. Displacement depends on both magnitude as well as direction.

iii. The diagram is given below:

In the above diagram,

AB is the distance

ACDB is the distance travelled by the object.

iv) Distance is a scalar quantity as it has only magnitude whereas Displacement is a vector quantity as it has both magnitude and displacement.

(i) The difference between uniform and non-uniform motion relies on, whether the velocity of the moving body is changing or not. If the velocity of the object changes to particular rate, then the motion is uniform, but if it increases or decreases at different points of time, then this movement is called as non-uniform motion.

(ii) In uniform motion, the object covers equal distance in equal time interval. In non-uniform motion, object covers equal distances in unequal time-intervals.

(iii)

From the first equation of motion,

v=u+at

here,

v = final velocity

u = initial velocity

a is the acceleration

t is the time

In the first table,

From Ist row, v = ?

⇒ v =2m/s + 4ms^-2 × 3s

⇒ v = 2m/s + 12 m/s

⇒ v = 14 m/s

from 2^nd row, u = ?

v = u + at

⇒ 20 m/s = u + 5ms^-2 × 2s

⇒ 20 m/s – 10m/s = u

⇒ u = 10 m/s

Now,

In the second table,

From the equation of motion,

S=ut + 1/2 at²

Where, s is the distance

“u” is the initial velocity.

“v” is the final velocity.

“t” is the time.

“a” is the acceleration

From Ist row, s = ?

⇒ S=ut + 1/2 at²

⇒ S = 5ms^-1 × 3s + 1/2 × 12ms^-2 × 3s × 3s

⇒ S=15m+ 54m

⇒ S = 69 m

From 2^nd row, a = ?

⇒ S=ut + 1/2 at²

⇒ 92m = 7ms^-1 × 4s + 1/2 × a × 4s ×4s

⇒ 92 m = 28 m + a × 8s²

⇒ a × 8s² = 92 – 28 m

⇒ a × 8s² = 64 m

⇒ a= 8 m/s²

Now, for the third table,

From second equation of motion,

v² = u²+2as

From Ist row ⇒ 8 = 4 × 4 + 2 × 3 × S

⇒ 8 = 16 + 6 × S

⇒ -8 = 6 × S

⇒ -8/6= S

⇒ S= -3/2 =-1.5 m

From 2^nd row ⇒ 10= u²+ 2× 5× 8.4

⇒ 10=u²+84

⇒ -74=u²

⇒ u=-8.6m/s

A. The minimum distance between the start and finish points of the motion of an object is called the displacement of the object.

Explanation:

As seen in the given figure,

The distance is not same as displacement. In fact, the displacement is the shortest distance between two given points.

B. Deceleration is negative acceleration.

Explanation:

Acceleration means increase in velocity. And, for decrease in velocity we have another term called “negative acceleration or deceleration”.

The figure shows the velocity time graph of an object:

C. When an object is in uniform circular motion, its velocity changes at every point.

Explanation:

In uniform circular motion, the speed of the object is same. Since, it direction is changing at every instant, hence its velocity changes. Because, velocity is speed with direction.

The object in uniform circular motion is shown here:

Here, the magnitude of both velocities is same.

D. During collision total momentum remains constant.

Explanation:

During collision the total momentum, remains the same.

The figure shows two objects here before & after collision:

E. The working of a rocket depends on Newton’s third law of motion.

Explanation: According to Newton’s third law of motion, every action has an equal and opposite reaction.

In a rocket, the burnt fuel releases gases, which push the rocket upwards. The direction of forces is given in the figure below:

As we know that

Where , G^'= new gravitational acceleration

i. When the point of action of the two equal and opposite forces is the same, then these do cancel out.

ii. But when the point of action of the two equal and opposite forces is different Though it located on the same body but separated by some distance between a the points of action of the two forces, then these forces don’t cancel out, but rather produce a couple. Example, closing a tap.

iii. But, if they are acting on different bodies, they cannot cancel out but rather produce motion.

For example, the downward weight is cancelled by the normal force while the force of the sun on the earth and its reaction, the force of the earth on the sun, do not cancel each other. We can see from diagram also.

Cricket ball is heavier than the tennis ball. Hence, the force required to stop a cricket ball is more as compared to tennis ball with the same velocity.

As we know, Force = Mass × acceleration

Here, force is directly proportional to mass.

So even if the velocity is same, the mass of leather ball is greater than that of tennis ball and the momentum (which is mass multiplied by velocity) and hence has more momentum and it is not easier to stop cricket ball.

In a uniform motion, the object travels equal distances in equal interval of time. Also, in uniform motion, the speed of the object is constant. The graph is given below:

Now, for an object at rest, the speed of the object is zero. As the time passes by, the speed is still zero. Hence, the object at rest is also considered as object in uniform motion.

1) Newton’s law of motion : Explanation with examples

According to the first law: If an object is at rest, it will remain in rest ,in motion will remain in motion unless an external unbalanced force act on it.

Example 1: Pushing a big rock, the rock will stay in place until you push it.

Example 2. When a rocket goes up in space, there is almost a perfect amount of earth gravity for ship to not come crashing down.

Example 3. When we shot the bullet in a space, it would travel in straight line until it reaches gravity of another planet.

2) Newton’s law of motion : Explanation with examples

According to 2^nd law: The force is directly proportional to rate of change of momentum.

Example 1: If a truck and bicycle did a short race at the same speed, then bicycle will win the race.

Example 2: For a long race truck will win the race because F=ma and a(acceleration) is more.

Example 3: If a dog is pulling a rock then acceleration is fully dependent on force of dog because mass of rock will not change.

3) Newton’s law of motion : Explanation with examples

According to the 3^rd law of motion, for every action there is an equal and opposite reaction.

Example 1. When we push the floor, the floor pushes back.

Example 2. Cars wheel produce friction trying to push and ground exerts an opposite force to push it.

Example 3. Rockets use fuel to push on ground ,which lifts them up. Rockets also rely on friction with air so that the fuel still works.

We know,

⇒ Average speed =

=

= 6m/s

∴ the average speed is 6 m/sec.

F= ma

Where m=16kg

a=3m/s²

F=16× 3= 48 N

If F= 48 N

m= 24kg

F= ma

48=24× a

a= 2 m/s²

Given:

Mass of bullet, m₁ = 10g = 0.01 kg

Speed of bullet, v₁ = 1.5 m/sec

Mass of wooden plank, m₂ = 90 g = 0.09 kg

Velocity of plank + bullet system = ?

Here, we will apply the law of conservation of momentum,

i.e. Final momentum = initial momentum

If we take bullet and thick wooden plank as a system then, initially only bullet is moving with speed of 1.5 m/s and plank is in rest.

∴ initial Momentum (p_i) = mass of bullet × velocity

= 0.01 kg ×1.5 m/sec

= 0.015 kgms^-1

⇒ p_i = 0.015 kgms^-1 ….(1)

Now, when the bullet hits the plank, then both the objects are attached.

So, new mass(M) = mass of bullet + mass of plank

= 0.01 kg + 0.09 kg

= 0.1kg

Then,

Final momentum, p_f = New mass (M) × (velocity of plank & bullet system)

⇒ p_f = 0.1kg × v….(2)

Now, from equation (1) & (2), we get,

P_i = p_f

⇒ 0.015 kgms^-1 = 0.1kg × v

⇒

⇒ v = 0.15 m/s

2.25 m/s

The average speed is given as:

⇒

⇒

⇒

Therefore, the average speed is 2.25 m/sec