Question

1: State how many significant figures there are in each of the following calculations, and indicate which is the limiting value:

Part (a) (18.7)^2:

^1- 1 (limited by 2)

^2-4 (limited by 18.7

^3- 2 (limited by 18.7

^4- 3 (limited by 18.7)

^5- None of these.

Part (b) (1.60 × 10^-19)(3712) :

1- 2 (limited by 3712)

2- 2 (limited by 1.60)

3- 4 (limited by 3712)

4- 3 (limited by 1.60)

5- None of these.

2: A student witnesses a flash of lightning and then t = 2.5 s later the student hears the associated clap of thunder.

Part (a) Sound travels at 343 m/s in the air. What distance from the student is the lightning strike, in meters?

Part (b) Light travels at 3.0 × 10⁸ m/s in the air. How long, t₁, in seconds did it take the light to reach the student's eyes after the lightning strike?

3: On a two-leg trip, a car travels the first leg, a distance D₁ = 49 miles, in a time t₁ = 1.1 hours, and travels the second leg, a distance D₂ = 140 miles, in time t₂ = 2.25 hours. Refer to the figure.

Part (d) What is the average speed for the whole trip in meters per second?

4: A student begins at rest and then walks north at a speed of v₁ = 0.55 m/s. The student then turns south and walks at a speed of v₂ = 0.92 m/s. Take north to be the positive direction. Refer to the figure.

Part (a) What is the student's overall average velocity v_avg, in meters per second, for the trip assuming the student spent equal times at speeds v₁ and v₂?

Part (b) If the student travels in the stated directions for 30.0 seconds at speed v₁ and for 20.0 seconds at speed v₂, what is the net displacement, in meters, during the trip?

Part (c) If it takes the student 5.0 s to reach the speed v₁ from rest, what is the magnitude of the student’s average acceleration, in meters per second squared, during that time?

Answer 1

1)

a)

Here we have as per the rule of significant figures in multiplying the 2 numbers,the product or the final answer should retain as many significant figures as there in the origial number with the least significant figure.

So,Here,

Here the significant figure in 18.7 is 3

and in 2 is 1

So,the final answer'ssignificant figure should limited by 1 significant figure.(Ie,limited by 2)

1(limited by 2) (Option 1)

b)

Here also,as per the rule of significant figures in multiplying the 2 numbers,the product or the final answer should retain as many significant figures as there in the origial number with the least significant figure.

Here the number of significant figures in is 3.

Also number of significant figures in 3712 is 4.

So,least number of significant figures for answer is 3.

So,here number of significant figures in answer limited by 1.60,which has least number of significant figures ie,3 comparitievely.

3 (Limited by 1.60) (Option 4)

2)

a)

Let the distance between the student and lightning strike be, m.

We have the velocity of light,

So,time taken by the light of lightnng to reach at student,

So,the time taken for the thunder(sound wave) to reach at the student from lightning strike,

We have the velocity of sound,

So,

On solving ,

b)

Here given the speed of light in air,

The distance between the thunder strike and the student

So,time taken for the light of lightning to reach at the student,

3)

d)Here,the distance travelled by the car in 1st leg , in time,

For the 2nd leg,Distance travelled, in time,

So,total distance travelled,

Total time taken,

So,average speed=Total distance/total time

We have,

So,

So,average speed,

4)

a)

The velocity by which the student travels to north,

Velocity with which the student travel to south after travelling north for time t,isLet time travelled to both north direction and then to south direction are equal to,

So,displacement of student to north direction,

displacement of student the student to south direction from B,

So,the total displacement travelled by the student,

ie,(Towards south direction)

So,the average velocity of student=Displacement/total time

(Here -ve sign indicates the net displacement is towards south direction.)

Or average velocity(Magnitude),

b)

Here the time travelled by student to north direction,

The velocity by which the student travels to north,

displacement of student in north direction,

the time travelled by student to south direction,

The velocity by which the student travels to south,

So.displacement of student in north direction,

So,total displacement of the student in journey,(Negetive sign shows that the net displacement is towards south direction.)

c)

Given the time taken from rest to velocity is t,

So,Here initial velocity,Final velocity,

Time taken,

So,Acceleration,