Question

If the position of a particle is changing with time as r=t²-2t (m). Find the velocity at t=2s.

• A. 2 m/s
• B. 3 m/s
• C. 0 m/s
• D. 4 m/s

Answer 1

The Correct Option is A

To find the velocity of a particle at a given time when its position as a function of time is provided, we need to differentiate the position function with respect to time. The velocity is the first derivative of the position function.

The given position function is:

\(r(t) = t^2 - 2t\)

The velocity \(v(t)\) is obtained by differentiating \(r(t)\) with respect to \(t\):

\(v(t) = \frac{d}{dt}(t^2 - 2t)\)

Calculating the derivative:

\(v(t) = \frac{d}{dt}(t^2) - \frac{d}{dt}(2t)\)

1. \(\frac{d}{dt}(t^2) = 2t\)
2. \(\frac{d}{dt}(2t) = 2\)

Thus, the velocity is:

\(v(t) = 2t - 2\)

We need to find the velocity at \(t = 2s\):

\(v(2) = 2(2) - 2 = 4 - 2 = 2 \, \text{m/s}\)

Therefore, the velocity at \(t = 2s\) is 2 m/s.

Hence, the correct answer is: 2 m/s.