Mathematics

Mathematics

Table of Contents

Chapter 13

Question # 293

Question # 344

Question # 365

Question # 405

Question # 445

Question # 486

Question # 786

Question # 886

Question # 1006

Question # 1067

Chapter 27

Question # 407

Question # 427

Question # 448

Question # 608

Question # 648

Question # 668

Question # 728

Question # 889

Question # 989

Question # 1109

Mathematics

Chapter 1

Question # 29

Letter to Grand Parents

I have just studied two new concepts, Velocity and Acceleration. Since both of them are associated with movement of objects, many of my classmates confuse them with each other. Velocity is the rate at which we cover some distance. If grandpa walks 1 meter, in one second then he will have the Velocity equaling 1 meter/sec. Similarly if our dog “Tom” is running and completes 10 meters in 2 seconds then the Velocity of our dog's commute will be 5meter/second.

The acceleration can be termed as the change in the velocity. If we continuously move with one speed then there is no acceleration i.e. no increase or decrease in our speed, but if we start to move a bit faster, than our speed will increase and thus we will accelerate.

I understood the difference between the acceleration and velocity with help of following example in our book.

ABC

In all the balls above, the speed will increase while falling from the hill. The acceleration or the rate of change of speed will differ. In hill A, the acceleration will be constant. In hill B, the acceleration will increase at first but will decrease as the ball reaches the end. The ball on Hill C will slowly start to accelerate and will increase in acceleration as it descends down the hill toward the end as the hill gets steeper.

Question # 34

Distance = 30 m

Time = 2 second

Average Speed = Total distance covered / travel time

Average speed = 30 / 2 = 15m / second

The rabbit covering 30 meters in 2 seconds will be running at an average speed of 15m per second.

Question # 36

Change of Velocity = 10m/s

Time Interval = 2 second

Acceleration = Change of velocity / time interval

Acceleration = 10 / 2 = 5 m / s2

The acceleration of the hamster which will attain speed of 10m/second from rest position in two seconds, will be 5m/s2

Question # 40

a)If both forces are acting in the same direction then they will produce a combine effect. We will add both the forces:

Net Force in Same Direction = Force A + Force B

Net Force = 30+20 = 50N having the same direction.

b)If both forces are acting in opposite direction then the net force will be difference in the forces and will be in the direction of higher force

Net Force in Opposite Direction = Force A - Force B

Net force = 30N-20N = 10N (in the direction of 30N Force)

Question # 44

The upward forces are 800N in the right hand scale. The sum of upward right hand forces and left hand forces must equal to the sum of total downward forces.

Let the left upward forces be “x”.

Then 800N + x = 400N ...