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The displacement of a particle is given by x = (t – 2)^{2} where x is in meters and t in seconds. The distance covered by the particle in the first 4 seconds is:
Displacement at t = 0 sec is: x = 4 meters
Displacement at t = 2 sec is: x = 0 meters
Displacement at t = 4 sec is: x = 2^{2} = 4 meters
∵ Particle changes direction at t = 2s
⇒ Particle travels from x = 4 m to x = 0 m in the first 2 sec and then from x = 0 m to x = 4 m position in the next two seconds
Distance travelled = 8 meters.
A vehicle travels half the distance L with speed V_{1}and the other half with speed V_{2}, then its average speed is
Let the vehicle travels from A to B. Distances, velocities, and time taken are shown. To calculate average speed we will calculate the total distance covered and will divide it by the time interval in which it covers that total distance.
Time taken to travel first half distance t_{1}
Time taken to travel first half distance t_{1}
Total time taken = t_{1 }+ t_{2}
We know that v_{av }= Average speed = Total Distance / Total Time
Which of the following statements about distance is true?
Displacement is the net distance between the initial position and final position, while the distance is the measure of the total path traveled during the entire journey.
Thus, distance is always equal to or more than displacement.
Which of the following quantity remains constant during the uniform circular motion?
When a body is in a uniform circular motion, its speed remains constant but its velocity, angular acceleration, angular velocity change due to a change in its direction.
The magnitude of average velocity is equal to the average speed if the motion of an object is along a straight line and in the same direction.
The magnitude of the average velocity of an object is equal to its average speed, only in one condition when an object is moving in a straight line as in this case the distance will be equal to the displacement.
Therefore, the given statement is true.
A particle is moving along a circle of radius R such that it completes one revolution in 40 seconds. What will be the displacement after 2 minutes 20 seconds?
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
The numerical ratio of average velocity to average speed is:
Therefore, the numerical ratio of average velocity to average speed is equal to or less than one but can never be more than one.
Two escalators move people up and down between floors of a shopping mall at the same rate, either up or down. What of the following statements regarding the motion of the escalators is true?
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.
The displacement of a body is zero. The distance covered
The displacement of an object be zero if distance is zero or if the final and initial positions are same. When the final and initial positions of an object are same, the distance is non zero.
Hence, answer is A. That means that distance covered may or may not be zero.
The displacement of a particle starting from rest (at t = 0) is given by s = 6t^{2}t^{3 }. The time in seconds at which the particle will attain zero velocity again, is
v = ds/dt
v = 12t  3t^{2}
0 = 3t (4  t)
⇒ t = 0 or 4
Here t = 0 is not realistic so at t = 4 the velocity will be zero.
The displacement is a relative term, therefore it can be positive, negative or even 0 depending upon the initial position.
If a body does not change its direction during the course of its motion, then ______.
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,
Which of the following is a one dimensional motion?
The motion of train running on a straight track is a motion in a straight line or in one direction. Hence it is one dimensional motion. Rest of the options are motions in three dimensions.
Suppose our school is 1 km away from our house, and we go to school in the morning, and in the afternoon we come back. Then, the total displacement for the entire trip is:
An object is in uniform motion along a straight line if it:
A man starts from his home with a speed of 4 km/h on a straight road up to his office 5 km away and returns to home, then the path length covered is:
5 km is the distance covered while going and 5 km while coming back.
⇒ Total path travelled = 10 km
A car covers a distance of 5 km in 5 mins, its average speed is equal to:
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
Which of the following is not an example of a rectilinear motion?
Rectilinear motion is another name for straightline 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.
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