Test: Displacement & Velocity - JEE MCQ

• 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

 Displacement is a vector quantity that depends on the initial and final positions of the particle. If a particle returns to its original position after moving, its displacement is zero, even though the distance covered is non-zero. Therefore, it's possible for the displacement to be zero if the particle returns to its starting point, while the distance traveled is non-zero. Hence, one of the two quantities, displacement or distance, may be zero, but not both.

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.

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

An upward, straight sloping line on a distance-time graph indicates constant speed because the distance covered is increasing at a steady rate over time. If the line was sloping upwards but becoming steeper, it would indicate speeding up. If the line was sloping upwards but becoming less steep, it would indicate slowing down. However, since the line is straight and upward, it suggests that the object is moving at a constant speed.