If the position of a particle is changing with time as r=t2-2t (m). Find the velocity at t=2s.
- 2 m/s
- 3 m/s
- 0 m/s
- 4 m/s
The Correct Option is A
Approach Solution - 1
\(v = \frac{dr}{dt}\)
In this case, the position function is given by r = t^2 - 2t (m). Taking the derivative with respect to time, we get:
\(v = \frac{dr}{dt} = \frac{d}{dt} (t^2 - 2t) = 2t - 2\)
To find the velocity at t = 2s, we substitute t = 2 into the expression for v:
\(v = 2t - 2 = 2(2) - 2 = 2 (\frac{m}{s})\)
Therefore, the velocity of the particle at t = 2s is 2 m/s, which is equivalent to option 1.
Answer. A
Approach Solution -2
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.