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Initial velocity of a trolley, u = 0 (at rest)

acceleration, a = 2 cms^-2 = 0.02 m/s² time t = 3s

As per 1 st law of motion

v = u + at

Here V means velocity of a trolley after 3s

V = 0 + 0.02 × 3

= 0.06 m/s.

∴ = 0.06 m/s.

Let the initial speed of the train be u = 90 Km/h

= 25 m/s.

Final speed of the train, v = 0 (train comes to rest)

acceleration a = 0.5 ms^-2

As per 3^rd law of motion

v² = u² + 2as

(0)² = (25)² + 2(0.5)s

s = train travelled distance

∴ s = \(\frac{(25)^2}{2(0.5)}\) = 625 m

Train will travel 625 km before it is brought to rest.

The quantity which is measured by the area occupied below the velocity-time graph is length = l

B) Throwing stone into the air, making some angle with the horizontal

Uniform circular motion is represented by the tip of the seconds hand of a watch. It is an accelerated motion.

The tip of the ‘seconds’ hand’ of a watch represents uniform circular motion. It is an accelerated motion.

u = 0 ms^-1  car is at rest. 

a = 0.1 ms^-2

t = 4 × 60 

= 240 sec. 

v = ? 

From, v = u + at 

v = 0 + 0.1 × 240 

Or v = 24 ms^-1

Maximum speed = 80 km/hr

Average speed = \(\frac{distance\,travelled}{time\,interval}\)

= \(\frac{400\,km}{10\,hr}\) = 40 m/hr

Ration = \(\frac{maximum\,speed}{average\,speed}= \frac{80\,km/hr}{40\,km/hr}=2\)

The motion of second’s hand represent uniform speed because as it is moving in a circular motion, its direction is changing at every point and hence uniform velocity will not be the case.

Correct option is C) A, D

Total time taken = 4s + 2s = 6s 

Average speed =\(\frac{Total\,distance\,travelled}{total\,time\,taken}\) = \(\frac{32}{6}\)= 5.33 ms^-1 

Therefore, the average speed of the object is 5.33 ms^-1.

Correct answer is (a) Half

Actual speed gives instantaneous speed of a body at any instant but average speed is the total distance covered by total time taken

In a 100 m race, the winner takes 10s to reach the finishing point. The average speed of the winner is 10 ms^-1.

Given: 

Distance = 20 km = 20,000 m 

Time = 45 min = 2700 s 

Formula: 

Average speed =\(\frac{Total\,Distance}{Total\,Time\,taken}\) 

Average speed = \(\frac{20 km}{45 min}\) = \(\frac{20,000 m}{2700s}\) = 

= \(\frac{200m}{27s}\)= 7.4 ms

Average speed = \(\frac{Total\,distance\,covered}{Total\,time\,taken}\)

= \(\frac{20\,m}{2\,secs}+\,\frac{20}{2}\) m/s = 10 m/s + 10 m/s = 20 m/s

The acceleration would be the area under the graph. 

Acceleration = \(\frac{vf\,-\,vi}{tf\,-\,ti}=\frac{(0-50)\,m/s}{(40-0)s}\) = 1.25m/s²

Similarity is that both the graphs shows uniform acceleration and dissimilarity is that in the irst graph the object starts from rest whereas in the second graph the object has some initial velocity.

1. scalar, vector 

2. speed 

3. retardation (or) deceleration 

4. displacement

The athlete was expected to take four rounds such that: line of finish = line of start 

This means, we are saying that athlete comes back to its initial position. This is only possible if there is change in direction. 

Without the change in direction a person can never reach back the initial point. 

Now, we know that change in direction means acceleration, hence motion is non uniform.

Distance travelled by the particle cannot be zero when displacement is not zero. 

Distance is the actual length of the path covered by a moving body irrespective of the direction in which body trace.

When a body moves from one position to another, then shortest (straight line) distance between initial and final positions of the body along with direction is displacement. 

|Displacement| \(\leq\) |Distance|

The above-mentioned relation implies that the distance is always greater than or equal to displacement. 

Hence, if |Displacement| ≠ 0, then Distance ≠ 0

The correct answer d) only iv

(a) Not true. Displacement can become zero when the initial and final position of the object is the same.

(b) Not true. Displacement is the shortest measurable distance between the initial and final positions of an object. It cannot be greater than the magnitude of the distance travelled by an object. However, sometimes, it may be equal to the distance travelled by the object.

The child reaches the point which he started. So the displacement is o.

A farmer moves along the boundary of a square field of side 10 m in 40s
2 minutes 20 seconds means 140 seconds.
Distance travelled by farmer
= \(\frac{40}{40}\) × 140 m
= 140 m.
∴ Farmer moves for 2 minutes 20 seconds. It means \(\frac{140}{40}\) = 3.5 rounds
From the original point, he moves for 2 minutes 20 seconds.
Case i) Original point means any point in the corner of the field. In this case he moves for 2 min 20 seconds from the diagonal of the field.
Displacement is equal to diagonal of the field displacement
= \(\sqrt{10^2+10^2}\)
= 14.1 m.
Case ii) Original point means any point in the middle of the side of the field.
∴ Displacement is equal to any side of the field = 10 m.
It means displacement is between any original point i.e., in between 14.1 m and 10 m.

False. 

The earth moves round the sun with uniform speed, but the velocity keeps changing.

Displacement refers to the measure of the shortest path between any two points whereas distance is the measurement of path between two points. The SI unit of both distance and displacement is meter (m).

The motion is accelerated.

SI unit of angular momentum is Radian per second (rad-s ^-1 ) 

Explanation: 

Since, 

Angular Velocity = \(\frac{Δθ}{t}\)

SI unit of 

• θ is radians 

• t is seconds 

Hence 

SI unit of Angular velocity is radians per second (rad s ^-1 )

a) Speed is defined as the distance travelled by the body in unit time. m/s is the SI unit of speed. 

b) i) Average speed is the sum total of the distance travelled by a body divided by the total time taken to cover that distance. Average speed = (total distance travelled)/(total time taken) 

ii) Uniform speed refers to constant speed of a moving body in which the body covers an equal distance in equal time intervals.

Yes, uniform circular motion is accelerated because the velocity changes due to continuous change in the direction of motion.

Acceleration: Acceleration of a body is defined as the rate of change of its velocity with time

Acceleration = \(\frac{change\,in\,velocity}{time\,taken}\)

SI unit: ms^-2 

For a body moving in a straight line we consider it to be moving with 

a) positive acceleration if the speed increases with time 

b) negative acceleration if speed decreases with time 

An example of uniform acceleration is: a ball rolling down a frictionless inclined plane.

a) Acceleration is defined as the rate of change in a body’s velocity with respect to time. SI unit of acceleration is m/s^2. 

b) A body is said to have a uniform acceleration when it travels in a straight line with its velocity increasing at equal intervals of time. Motion of a free falling ball is an example of uniform acceleration.

(a) Acceleration of a body is defined as the rate of change of its velocity with time. SI unit of acceleration is m/s² .

(b) A body has uniform acceleration if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time. For example: Motion of a freely falling body.