Ans. We define: Uniform velocity (or constant velocity): If a body moves over equal distances in equal intervals of time, however small, in a particular direction, it is said to move with uniform velocity. Variable velocity: When a body traverses unequal distances in equal intervals of time, or when its direction of motion changes, it is said to move with a variable velocity. Difference: In uniform velocity, equal distances are covered in equal intervals of time, but in variable velocity, unequal distances are covered in equal intervals of time. Also in uniform velocity the direction of motion does not change, but in variable velocity the direction may change. Acceleration: The time rate of change of velocity is called acceleration. The change in velocity can occur due to change in speed or in direction or in both—defined as variable velocity. SI units of velocity and acceleration: Velocity: m/sec (mS-1) Acceleration: m/sec2 (mS-2)
Q.2 An object is thrown vertically upward. Discuss the sign of acceleration due to gravity, relative to velocity, while the object is in air.
Ans. Since direction of initial velocity is upward. So g will be negative, relative to velocity. For downward motion, g is positive with reference to the direction of initial velocity.
Q.3 Can the velocity of an object reverse direction when acceleration is constant? If so, give an example.
Ans. Yes. For bodies freely falling back in air. If a body moves upward, finally reverse direction and moves down. The acceleration due to gravity is constant for both directions of motion.
Q.4 Specify the correct statement:
a. An object can have a constant velocity even its speed is changing.
b. An object can have a constant speed even its velocity is changing.
c. An object can have a zero velocity even its acceleration is not zero
d. An object subjected to a constant acceleration can reverse its velocity.
Ans. Statements (b), (c) & (d) are correct. Examples of: (b) circular motion. (c) total (upward & downward) velocity is zero moving under g. (d) in the air, bodies freely falling back.
Q.5 A man standing on the top of a tower throws a ball straight up with initial velocity vi and at the same time throws a second ball straight downward with the same speed. Which ball will have larger speed when it strikes the ground? Ignore air friction.
Ans. Upward thrown ball will have larger speed when it strikes the ground. Since it will take more time and move larger downward distance under g.
Q.6 Explain the circumstances in which the velocity v and acceleration a of a car are
(i) Parallel (ii) Anti-parallel (iii) Perpendicular to one another
(iv) v is zero but a is not (v) a is zero but v is not zero
Ans. (i) The car moving with increasing speed. (ii) The car moving with decreasing speed. (iii) Moving a curved or circular path. (iv) When sudden brakes are applied. (v) Moving with uniform velocity.
Q.7 Motion with constant velocity is a special case of motion with constant acceleration.Is this statement true? Discuss.
Ans: This statement is true because when the body moves with uniform velocity then the change in velocity is zero which continuously remain zero. so the body moves with this constant zero acceleration in its uniform motion.
Q.8 Find the change in momentum for an object subjected to a given force for a given time and state law of motion in terms of momentum.
Ans. F = m a = m (vf - vi ) = mvf - mvi = time rate of change of momentum t t so 2nd law of motion in terms of momentum: “Time rate of change of momentum of a body equals the applied force”.
Q.9 Define impulse and show that how it is related to linear momentum.
Ans. Impulse: “The product of force and time for which it acts on a body”. Impulse = F x t = m a t = m (vf - vi ) x t = m (vf - vi ) t It shows the impulse equals the change in linear momentum of a body.
Q.10 State the law of conservation of linear momentum, pointing out the importance of isolated system. Explain, why under certain conditions, the law is useful even though the system is not completely isolated?
Ans. Law of conservation of linear momentum: “The total linear momentum of an isolated system remains constant”. m1 v1 + m2 v2 = m1 v1′ + m2 v2′ (m1 v1 + m2 v2 ) - (m1 v1′ + m2 v2′ ) = 0 An isolated system is free from external forces. External influence may effect the mutual interaction. ii) If a system is not completely isolated but external forces are very small comparing with mutual interacting forces, the law is useful. e.g. when calculating pressure of a gas and applying conservation of linear momentum, neglecting g, the external force.
Q.11 Explain the difference between elastic and inelastic collisions. Explain how would a bouncing ball behave in each case? Give plausible reasons for the fact that K.E. is not conserved in most cases?
Ans. We define, Elastic collision: “The interaction in which both momentum and kinetic energy conserve”. Inelastic collision: “The interaction in which kinetic energy does not conserve”. Difference: In elastic collision law of conservation of momentum and kinetic energy holds but in inelastic collisions these two laws does not hold.
Bouncing ball: In elastic collision, the bouncing ball should rebound to the original height. In inelastic collision, the bouncing ball will not rebound or will rebound to a smaller height from where it is dropped. Plausible reasons: In most collisions, some KE change into heat, sound and in their deformation due to frictions.
Q.12 Explain what is meant by projectile motion. Derive expressions for
a. the time of flight b. the range of projectile.
Show that the range of projectile is maximum when projectile is thrown at an angle of 45o with the horizontal.
Ans. Projectile motion: “The motion of a body moving under the action of gravity and moving horizontally at the same time”. Time of flight: We have S = 0 ; vi = vi sinθ ; a = -g Using S = vi t + ½ a t2 ⇒ 0 = vi sinθ t – ½ g t2 or t = 2 vi sinθ g Range of the projectile: We have S = R , vx = vi cosθ, t = 2vi sinθ Using S = v t g ⇒ R = vi cosθ x 2 vi sinθ = vi2 2 sinθ cosθ g g or R = v sin 2θ g for maximum range, sin 2θ should have maximum value ( i.e.) = 1 sin 2θ = 1 ⇒ 2θ = 90o ⇒ θ = 45o
Q.13 At what point or points in its path does a projectile have its minimum speed, its
maximum speed?
Ans. A projectile will have its minimum speed at the highest point (maximum height). It has its maximum speed at the start and end of the projectile motion.
Q.14 Each of the following questions is followed by four answers, one of which is correct answer. Identify that answer.
i. What is meant by a ballistic trajectory?
a. The paths followed by an un-powered and unguided projectile.
b. The path followed by the powered and unguided projectile.
c. The path followed by un-powered and guided projectile.
d. The path followed by powered and guided projectile.
ii. What happens when a system of two bodies undergoes an elastic collision?
a. The momentum of the system changes.
b. The momentum of the system does not change.
c. The bodies come to rest after collision.
d. The energy conservation law is violated.
Ans. (i) The correct answer is (a). A ballistic trajectory means the paths followed by an un-powered and un-guided projectile. (ii) The correct answer is (b). In elastic collision, the momentum of the system does not change.
i like your answers but i think that these are too short please elaborate the answers
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