Velocity-Time Area and Displacement
The relationship between velocity, time, and displacement is fundamental in kinematics. The velocity-time graph plots velocity against time.
The area under the velocity-time curve between two specific time points, say \(t_1\) and \(t_2\), represents the total change in position, which is the displacement, during that interval. Mathematically, this is expressed as the definite integral of velocity \(v(t)\) with respect to time \(t\) from \(t_1\) to \(t_2\):
Area \(= \int_{t_1}^{t_2} v(t) \, dt = \Delta x\)
Where \(\Delta x\) is the displacement.
The question specifically asks for the magnitude of displacement.
Identifying the Correct Quantity
- The area under the velocity-time curve directly calculates the displacement.
- Displacement is a vector quantity, representing the change in position.
- The question asks for the magnitude of this displacement, which is a scalar value.
- Therefore, the area under the velocity-time curve equals the magnitude of the displacement.
Options like force and acceleration are different physical quantities not directly represented by this area.
Average velocity describes the overall velocity change but isn't the area itself.
The correct answer is the magnitude of displacement.
Similar Questions
Acar moving along a straight path slows down and stops. The car is under which type of motion?
What is the path of an object when it is in uniform motion?
Why do cars have treaded tyres?
- Neha swims in a pool that is 50 metres long. She covers 100 metres in 1 minute by swimming from one end of the pool to the other and back along the same straight path. Find her average velocity (in m/s).
- A force acts on a 4 kg body at rest and produces an acceleration of 3 m/s². The final velocity after 5 seconds is:
- A car falls off a ledge and drops to the ground in 0.8 s. Take g = 10 m/s² (for simplifying the calculations). How high is the ledge from the ground?
Pihu starts her car at 9 a.m. to reach her office, which is 20 km away. She covers the first 10 km in 30 minutes and reaches her office at 10 a.m. Pihu's motion is _______.
Which of the following is an example of uniform motion?
Which of the following physical quantities represents the rate of change of velocity?
Which of the following physical quantities is equivalent to the total path length covered by a moving body?
Important Questions from Motion
An object is covering distance in direct proportion to the square of time elapsed. What conclusion can be drawn about the motion of the object?
If the distance time graph of the motion of an object is a straight line but not parallel to the time axis, then it may be concluded that the object is moving with a:
Which of the following changes when a body performs uniform circular motion?
Vehicles have treaded tires so that it_______.
If the initial velocity of an object thrown upwards is 14 m/s, then the time taken for the object to reach its highest point will be_______. (a = 9.8 m/s2)
