Question

Question(48)
A particle traversed along a straight line for first half time with velocity 20kmph. For the remaining part, half of the distance is traversed with velocity 30kmph
and other half distance with velocity 40kmph. Find the mean velocity (in kmph) of the particle.​

Answer 1

Answer:

Explanation:

See the pics

Answer 2

Answer- The above question is from the chapter 'Kinematics'.

Some important terms and formulae:-

1. Velocity- It is the displacement per unit time.

S.I. Unit of Velocity- m/s

It is a vector quantity as it possesses magnitude and direction.

2. Acceleration- It is the rate of change of velocity.

S.I. Unit of Acceleration- m/s²

It is also a vector quantity.

Negative acceleration is called retardation.

3. Distance- It is the path length transversed by an object.

S.I. Unit of Distance- m

It is a scalar quantity.

4. Displacement- It is the shortest distance between the initial and final point.

S.I. Unit of Displacement- m

It is a vector quantity.

5. Equations for uniformly accelerated motion-

Let u = Initial velocity of a particle

v = Final velocity of a particle

t = Time taken

s = Distance travelled in the given time

a = Acceleration

1) v = u + at

2) s = $\frac{1}{2}$ at² + ut

3) v² - u² = 2as

6. Average Speed = Total distance ÷ Total time

7. Average Velocity = Total displacement ÷ Total time

8. Some basic formulae using calculus method:

1) Velocity = $\frac{dx}{dt}$

2) Acceleration = $\frac{dv}{dt}$

3) Acceleration (when x is given) = $v \frac{dv}{dx}$

Given question: A particle traversed along a straight line for first half time with velocity 20 kmph. For the remaining part, half of the distance is traversed with velocity 30 kmph and other half distance with velocity 40 kmph. Find the mean velocity (in kmph) of the particle.​

Answer: This question can be solved by using the formula:

Mean velocity = $\frac{2v(v_{1} + v_{2})}{v_{1} + v_{2} + 2v}$

Let v = 20 km/h

v₁ = 30 km/h

v₂ = 40 km/h

Mean velocity = $\frac{40 \times 70}{110}$

Mean velocity = 25.45 km/h

∴ Mean velocity of particle is 25.45 km/h.