Motion In A Straight Line

Given, From the 3 rd equation of motion, This is the equation of the parabola. Hence, the velocity- displacement curve is parabola in nature.

Time of ascent = Time of descent = = 2 s
u + (-gt) i.e. 0 = u - 10 2 i.e. u = 20 m

Let be the required time.
Distance covered by car, S =
Distance covered by scooter = 96 + S = 20 t
i.e. = 0
Solving = 8 s.

Distance moved = 26 + 26 + 26 = 78 m

Displacement = 26 - 26 - 26 = - 26 m
Magnitude of displacement = 26 m

Both the stones will have the same speed when they hit the ground.

If be the velocity of water and be the velocity of motorboat in still water.
The distance covered by motorboat in moving downstream in is
...(i)
Same distance covered by motorboat in moving upstream in is
...(ii)
From Eqs. (i) and (ii), we have



Time taken by the motorboat to cover the same distance in still water is

Relative velocity of passenger w.r.t. train

Relative velocity of the passenger w.r.t. the observer is zero.

The height to which the balls

We know that

(if
By Newton's second law of motion

where (body is at rest)
So,

Key Idea Average velocity
In , the distance covered by the body
Here,

Slope of x-t graph gives speed
The graph is steepest between Q and R
velocity is maximum at R.

Given line have positive intercept but negative slope. So its equation can be written as, where By differentiating with respect to time we get, Now substituting the value of ??? i.e., the graph between a and x should have positive slope but negative intercept on acceleration axis.

Let, the length of the escalator be .
Velocity of the girl,
Velocity of the escalator,
On moving escalator.

or,
or,
Since,
Therefore,

Dimensional analysis helps in deriving expressions that are dimensionally consistent. We analyze each of the options: - Option (1) cannot be derived directly using dimensional analysis as it involves unknown constants and factors not defined by basic physical dimensions. - Option (2) is the standard kinematic equation for displacement under constant acceleration, which can indeed be derived using dimensional analysis, as the units of each term are consistent with displacement. - Option (3) is a solution to simple harmonic motion, and while it is physically correct, its dimensional consistency needs more information for derivation. - Option (4) involves exponential growth, and dimensional analysis does not provide a simple way to deduce this relationship. Thus, the correct answer is the kinematic equation , which is a standard result in mechanics.

Step 1: Understanding the Question:
The problem asks for the average speed of a car that travels two equal distances at different constant speeds.
Step 2: Key Formula or Approach:
Average speed is total distance divided by total time.
When two equal distances ( ) are covered at speeds and , the average speed is the harmonic mean of the two speeds:

Step 3: Detailed Explanation:
Given:
Speed for first half,
Speed for second half,
Substituting these values into the harmonic mean formula:



Step 4: Final Answer:
The average speed of the car is 44.44 km/h.