Test: Displacement & Velocity - 1 - JEE MCQ

Another solution :-

• Displacement is the shortest length between the starting and the end pointing of a journey, whereas the distance is the actual length of the path travelled.
• Hence, the distance will always be equal to or greater than the displacement.
• So, the ratio of displacement to distance will be always less than or equal to 1, since the denominator(distance) is either greater than or equal to the numerator (displacement).

The speeds of the body when it moves from O to A  is

The speeds of the body when it moves from B to C  is

The correct option is B Both cannot be zero
If the location of a particle has changed then it certainly did some displacement and if it has undergone some displacement, then it has travelled some distance too.

1 revolution in 40 seconds
In 1 second it covers = 1/40 revolution
In 140 sec = 1/40 * 140 =7/2 rotation = 3 and half rotation

Then the particle will be on the diametrically opposite end. 

Therefore, Displacement = R + R = 2R

• When an object is moving along a straight path, the magnitude of average velocity is equal to the average speed.
• Therefore, the numerical ratio of average velocity to average speed is one in a straight line motion.
• But, during curved motion, the displacement < distance covered, so the velocity < speed.

​Therefore, the numerical ratio of average velocity to average speed is equal to or less than one but can never be more than one. 

As the particles are moving at the same rate, their speed is the same but velocities will be different beacuse their directions will be different.

Apply differentiation
v = ds/dt
v = 12t - 3t²
0 = 3t (4 - t)
⇒ t = 0 or 4
Here t = 0 is not realistic so at t = 4 the velocity will be zero.
Thus, the particle will attain zero velocity at the time of 4 seconds.

Displacement (x): The change in the position of an object is called displacement.

• Displacement is a one-dimensional quantity representing the smallest separation between two defined points.
• The standard unit of displacement in the International System of Units (SI) is the meter (m).

Velocity (V): The rate of change of displacement is called velocity. It is a vector quantity. 

• The SI unit of velocity is called m/s and the CGS unit is cm/s.
• The slope of the displacement-time graph gives the velocity

Instanteneous  Velocity(v)  = dx/dt

Hence, dx = v⋅dt
Displacement (X) = 

Thus the area under the velocity-time graph gives the displacement. Similarly, the area under-speed time graph gives the total distance travelled.

Area under the velocity-time curve represents displacement.

To get exact position at t, we need to calculate the area of the shaded part in the curve as shown below

Area of parellogram = ½ × (Sum of parallel sides) × distance between them.

⇒ Area of parellogram = ½ × (15 + 5) × 100

⇒ Area of parellogram = ½ × 20 × 100 = 1000 m

Hence the correct option is 1000 meter.

Since the object does not change its direction it means that the object is traveling in a straight line.
⇒ The path length and displacement will be equal.

1 km = 1000 m and 1 hr = 3600 sec.

Therefore,

Calculation: 

the first half an hour when the car speed = 60 km/h.

the next half an hour when the car speed = 45 km/h.

Distance covered in the first half an hour = Speed × Time

Distance covered in the first half an hour = 60 km/h × 0.5 h

Distance covered in the first half an hour D1 = 30 km

Next, let's calculate the distance covered in the next half an hour when the car is moving at a speed of 45 km/h.

Distance covered in the next half an hour = Speed × Time

Distance covered in the next half an hour = 45 km/h × 0.5 h

Distance covered in the next half an hour D2 = 22.5 km

Total distance  = Distance covered in the first half an hour + Distance covered in the next half an hour

Total distance covered = 30 km + 22.5 km

Total distance covered = 52.5

• Displacement quantifies both direction and distance of an imaginary motion along a straight line from the initial position to the final position of the point.
• Here, since the same amount of distance is covered in the opposite direction, the total displacement for the entire trip is zero. 

When velocity is uniform, velocity-time graph is straight line parallel to time axis. So, the slope is zero.

The path length covered by the man is the total distance traveled, not the displacement. Here’s the breakdown:

1. Distance from home to office: 5 km
2. Return distance from office to home: 5 km

So, the total path length covered is:

5 km (to office)+5 km (back home)=10 km

Therefore, the correct answer is:

4. 10 km

Let t1 and t2 be the time taken for Jagadeesh to go to school and then back home. If s is the displacement, then

Total time taken

Total displacement=2 s
Avg Speed = 

5 km is the distance covered in 5 mins, which means 1 km is the distance covered in 1 min
Hence, it will travel 60 km in 60 mins, i.e. speed = 60 km/hr

Given,

v1=40 km/hr and v2=60 km/hr.

The average velocity when the car covers equal displacements would be,

Rectilinear motion is another name for straight-line motion. 
A body is said to experience rectilinear motion if any two particles of the body travel the same distance along two parallel straight lines.

A car moving in a circular path changes its direction at every instant. Thus, it is not the rectilinear motion.

The displacement made by the girl is AB