Question:
Mathematically prove that the distance (S) travelled by an object is the average mean of initial velocity(u) and final velocity(v) having constant acceleration(a) in the direction of motion in a straight line.
Answer:
: To prove S = ½(u+v)t
We know that v = u + at
and 2aS = v2 - u2
⇒ 2aS = (v-u)(v+u) [∵ Algebraic identity (a2 - b2) = (a+ b)(a -b) ]
⇒ 2aS = (v+u)at [ using v - u = at]
⇒ 2S = (v+u)t
or S = ½(u+v)t
⇒ (u+v)/2 is the average velocity.
Motion
Q 1.
Derive graphically the equation of motion for position-velocity relation of a body moving with uniform acceleration.
Q 2.
A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
Q 3.
When will you say a body is in (i) uniform acceleration? (ii) nonuniform acceleration?
Q 4.
A particle moves over three quarters of a circle of radius r.What is the magnitude of its displacement ?
Q 5.
A cyclist cycles for t second at a speed of 3 m/s and then for the same time at a speed of 5 m/s along a straight road due north. What is the average speed of the cyclist?
Q 6.
The mass of an empty 40 litre petrol tank of a vehicle is 8.0 kg.What will be its mass when filled completely with a fuel of density 700
Q 7.
What is represented by the graphs in Fig.?
.
Q 8.
Write the three equations of uniformly accelerated motion. Give the meaning of each symbol in them.
Q 9.
Calculate the greatest and the least pressure exerted by a metal block of size 20 cm x 8 cm x 5 cm and having a mass of 5 kg.
Q 10.
Why is a slight blow on a cork of bottle fully filled with a liquid sufficient to break the bottle ?
Q 11.
A ship is moving at a speed of 56 km/h.One second later,it is moving at 58 km/h.What is its acceleration ?
Q 12.
Under what conditions(s) is the magnitude of average
Q 13.
A body starts from rest.What is zero ?
Q 14.
What is pressure in case of fluids ? What is Pascal’s law ?
Q 15.
What will be the initial velocity of an object under free fall?
Q 16.
Draw speed-time graph for a body (i) at rest (ii) in uniform motion (iii) in uniformly accelerated motion.Discuss the results briefly.
Q 17.
A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg.The area of the piston carrying the load is
.What maximum pressure would the smaller piston have to bear ?
Q 18.
Define buoyant force.What is its unit ?
Q 19.
Air is a fluid and our bodies displace air.As a result of this,a buoyant force is acting on each one of us.
(a)What is the approximate density of your body ?
(b) What is your approximate volume ?
(c) Estimate the magnitude of the buoyant force on you due to the air displaced.Consider your mass to be 75 kg.
(d)Does it mean that your weight is more than the scale reading ?
(Given density of air,pa =
)
Q 20.
Name the quantity that represents rate of change of velocity ?
Q 21.
Why does a person feel pain when he stands on a pile of gravel than when he stands on a bed of sand ?
Q 22.
When a plastic block is released under water,it never stays under water but instead comes to the surface of water.Explain why ?
Q 23.
What conclusion do you draw when displacement-time graph of a body is as shown in Fig.?
Q 24.
If velocity-time graph of a body is as shown in Fig.,what is the nature of motion ?
Q 25.
A bottle can hold 100 g of water at 4°C.What mass of sea water (density =
) can it hold ?
Q 26.
What force acting on an area of
will produce a pressure of 500 Pa ?
Q 27.
What is the relationship between the buoyant force on an object and the liquid displaced by it ?
Q 28.
The density of turpentine oil is
.What will be its relative density ?
Q 29.
A car travels along a straight line for first half time with speed 40 km/h and the second half time with speed 60 km/h. Find the average speed of the car.
Q 30.
A train starting from rest moves with a uniform acceleration of 0.2
for 5 minutes.Calcualte the speed acquired and the distance travelled in this time.
Q 31.
What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis ?
Q 32.
Use graphical method to derive the relation
-
= 2 as,where the symbols have their usual meanings.
Q 33.
State velocity-time relation in uniformly accelerated motion. Use graphical method to obtain this relation.
Q 34.
Calculate the pressure when a force of 200 N acts on an
Q 35.
Why is it easier to swim in sea water than in river water ?
Q 36.
What is meant by scalars and vectors?
Q 37.
A particle moves along the x axis from A to B. Which Of the following values of the initial and final coordinates, which results in a negative displacement?
(a) A = 4m, B = 6m
(b) A = −4m, B = −2m
(c) A = −4m, B = −8m
(d) A = −4m, B = 2m
Q 38.
A body travels a distance of 15 m from A to B and then moves a distance of 20 m at right angles to AB.Calculate the total distance travelled and the displacement.
Q 39.
Distinguish between speed and velocity.
Q 40.
A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is
in the downward direction,what will be the height attained by the stone and how much time will it take to reach there ?
Q 41.
The speed-time graph for a car is shown is Fig.
(a) Find how far does the car travel in the first 4 seconds.Shade the area on the graph that represents the distance travelled by the car during this period.
(b) Which part of the graph represents uniform motion of the car ?
.
Q 42.
An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the Earth.
Q 43.
What is the SI unit of displacement ?
Q 44.
A nail is driven into a wooden board by using a hammer.The impact of the hammer on the head of the nail produces a thrust of 25 N.If the area of the head is
and of the tip
,find the pressures on the head and the tip of the tail.
Q 45.
A block of wood is kept on a table top.The mass of the wooden block is 5 kg and its dimensions are 40 cm x 20 cm x 10 cm.Find the pressure exerted by the wooden block on the table top if it is made to lie on the table with its sides of dimensions (a) 20 cm x 10 cm (b) 40 cm x 20 cm. Given g =
.
Q 46.
Calculate the mass of air enclosed in a room of length,breadth and height equal to 5 m, 3 m and 4 m respectively.Density of air =
.
Q 47.
A body of 2.0 kg floats in a liquid.What is the buoyant force on the body ?
Q 48.
Why Is it difficult to hold a school bag having strap made of thin and strong string ?
Q 49.
What is the density of water at 4°C ?
Q 50.
Why is a bucket of water lighter when in water than when it is taken out of water ?
