Q: If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?

Acceleration does not mean speeding up or speeding down. It means the change of velocity either in direction or in magnitude.

Q: (a) Give example where the velocity of a particle is zero but its acceleration is not zero.(b) Give example where the velocity is opposite in direction to the acceleration.(c) Give example where the velocity is perpendicular to the acceleration.

(a) At the highest point when a particle is thrown vertically upwards.(b) While going up when a particle is thrown vertically upwards. (c) At the highest point of a full projectile.

Q: Shows the x coordinate of a particle as a function of time. Find the signs of vx and ax at t=t1 , t=t2 and t=t3.

Slope of the x−t graph gives the velocity and change in the slope gives the acceleration. At t=t1, Slope = Positive ⇒ Velocity = Positive Slope is increasing ⇒ Acceleration = Positive At t=t2, Slope = Zero ⇒ Velocity = Zero Slope is increasing ⇒ Acceleration = Negative At t=t3, Slope = Negative ⇒ Velocity = Negative Slope is increasing ⇒ Acceleration = Positive

Q: The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without putting more petrol or less petrol into the engine?

Yes, it is possible to accelerate a car without putting more petrol or less petrol in the engine. This can be done by driving the car on a circular or curved track at a uniform speed.

Q: Rain is falling vertically. A man running on the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avoid the vertical sun-rays. Explain.

The speed of rain is less, so as we run, the direction of the relative velocity of the rain changes. But as the speed of light is very high, there is a measurable change in the relative velocity of light w.r.t. a person due to the relative motion between the sunrays and the person.

Q: A motor car is going due north at a speed of 50 km/h. It makes a 90° left turn without changing the speed. The change in the velocity of the car is about:

Final velocity, Vf=−50i^ km / h Initial velocity, Vi=−50i^ km / h Change in velocity, ∆V=Vf−Vi ∣∆V∣=502+502+2×50×50cos(90°)=70 km /hIt is towards southwest, as shown in the figure.

Question 1

When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speed are all equal. Comment on this statement.

Accepted Answer

Constant velocity means that a particle has the same direction and speed at every point. So, its average velocity and instantaneous velocity are equal. Its speed being a scalar quantity is equal in magnitude only.

Question 2

A car travels at a speed of 60 km/hr due north and the other at a speed of 60 km/hr due east. Are the velocities equal? If no, which one is greater? If you find any of the questions irrelevant, explain.

Accepted Answer

No, as the directions of the cars are different, their velocities are not equal, as velocity is a vector quantity.We cannot compare velocities on the basis of direction only, so the question is irrelevant.

Question 3

The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion .

Accepted Answer

Motion of a projectile at the highest point of its path: Because at this point, the projectile has only horizontal component of velocity. So, it can have velocity towards west and acceleration in the vertically downward direction.

Question 4

Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. The particle B has an acceleration 2a for the first and a for the second half. Which particle has covered larger distance?

Accepted Answer

From the velocity-time graph, we have: Distance covered by A=(21​×2t​×2at​+21​×2t​×2at​+2t​×2at​)=2at2​ Distance covered by B=(21​×at×2t​+at×2t​+21​×2at​×2t​)=87​at2  ∴  Distance covered by A<  Distance covered by B

Question 5

If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?

Accepted Answer

Acceleration does not mean speeding up or speeding down. It means the change of velocity either in direction or in magnitude.

Question 6

(a) Give example where  the velocity of a particle is zero but its acceleration is not zero.(b) Give example where the velocity is opposite in direction to the acceleration.(c) Give example where the velocity is perpendicular to the acceleration.

Accepted Answer

(a) At the highest point when a particle is thrown vertically upwards.(b) While going up when a particle is thrown vertically upwards. (c) At the highest point of a full projectile.

Question 7

Shows the x  coordinate of a particle as a function of time. Find the signs of vx​  and ax​  at t=t1​ , t=t2​  and t=t3​.

Accepted Answer

​ Slope of the x−t graph gives the velocity and change in the slope gives the acceleration.  At t=t1​,  Slope = Positive ⇒ Velocity = Positive  Slope is increasing ⇒ Acceleration = Positive  At t=t2​,  Slope = Zero ⇒ Velocity = Zero  Slope is increasing ⇒ Acceleration = Negative  At t=t3​,  Slope = Negative ⇒ Velocity = Negative  Slope is increasing ⇒ Acceleration = Positive ​

Question 8

The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without putting more petrol or less petrol into the engine?

Accepted Answer

Yes, it is possible to accelerate a car without putting more petrol or less petrol in the engine. This can be done by driving the car on a circular or curved track at a uniform speed.

Question 9

Rain is falling vertically. A man running on the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avoid the vertical sun-rays. Explain.

Accepted Answer

The speed of rain is less, so as we run, the direction of the relative velocity of the rain changes. But as the speed of light is very high, there is a measurable change in the relative velocity of light w.r.t. a person due to the relative motion between the sunrays and the person.

Question 10

A motor car is going due north at a speed of 50 km/h. It makes a 90° left turn without changing the speed. The change in the velocity of the car is about:

Accepted Answer

Final velocity, Vf​​=−50i^  km / h  Initial velocity, Vi​​=−50i^  km / h  Change in velocity, ∆V=Vf​​−Vi​​ ∣∆V∣=502+502+2×50×50cos(90°)​=70 km /hIt is towards southwest, as shown in the figure.

Question 11

In figure shows the displacement-time graph of a particle moving on the X-axis.

Accepted Answer

(d) The particle moves at a constant velocity up to a time t0​ and then stops.The slope of the x–t graph gives the velocity. In the graph, the slope is constant from t = 0 to t = t0​ , so the velocity is constant. After t = t0​ , the displacement is zero; i.e., the particle stops.

Question 12

A particle has a velocity u towards east at t = 0. Its acceleration is towards west and is constant. Let xA​  and xB​  be the magnitude of displacements in the first 10 seconds and the next 10 seconds .

Accepted Answer

(d) The information is insufficient to decide the relation of xA​  with xB​ .As velocity and acceleration are in opposite directions, velocity will become zero after some time (t) and the particle will return.∴0=u−at  ⇒t=au​ Because the value of acceleration is not given, we cannot say that the particle will return after/before 10 seconds.

Question 13

A person travelling on a straight line moves with a uniform velocity v1​  for a distance x and with a uniform velocity v2​  for the next equal distance. The average velocity v is given by:

Accepted Answer

(c) v2​=v1​1​+v2​1​. Velocity is uniform in both cases; that is, acceleration is zero.x=v1​t1​⇒t1​=v1​x​x=v2​t2​  ⇒t2​=v2​x​ Total displacement, x=v2​t2​⇒t2​=v2​x​ Total time, x′=2x∴  Average velocity, t=t1​+t2​⇒v2​=v1​1​+v2​1​

Question 14

A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is:

Accepted Answer

(d) g downwardGravity is the only force acting on the stone when it is released. And, we know that gravity is always in the downward direction.

Question 15

A person standing near the edge of the top of a building throws two balls A and B. the ball A is thrown vertically upward and B is thrown vertically downward with the same speed. The ball A hits the ground with a speed vA​ and the ball B this the ground with a speed vB​ . We have:

Accepted Answer

(c) vA​  = vB​ Total energy of any particle = 21​mv2+mgh Both the particles were at the same height and thrown with equal initial velocities, so their initial total energies are equal. By the law of conservation of energy, their final energies are equal. At the ground, they are at the same height. So, their P.E. are also equal; this implies that their K.E. should also be equal. In other words, their final velocities are equal.

Question 16

A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction:

Accepted Answer

(a) Due north.If the man swims at any angle east to the north direction, although his relative speed will increase, he will have to travel a larger distance. So, he will take more time.If the man swims at any angle west to the north direction, his relative speed will decrease. So, he will take more time.

Question 17

In the arrangement shown in figure the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed:

Accepted Answer

(b) v=cos(θ)u​Along the string, the velocity of each object is the same.v=cos(θ)u​

Question 18

Consider the motion of the tip of the minute hand of a clock. In one hour:

Accepted Answer

(a) The displacement is zero.(d) The average velocity is zero.Displacement is zero because the initial and final positions are the same.Average velocity =  Total time Displacement ​=0 Distance covered = 2πr ≠ 0Average speed =  Total time taken Distance travelled​=0

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