Question

1. a particle moves along the x - axis and its coordinates vary with time according to the relation x = t² - 2t, where x is measured in meters and t is in seconds. find the velocity of the particle at t = 2s.

Explanation:

Step1: Recall velocity - displacement relation

Velocity $v=\frac{dx}{dt}$. Given $x = t^{2}-2t$.

Step2: Differentiate $x$ with respect to $t$

Using the power - rule $\frac{d}{dt}(t^{n})=nt^{n - 1}$, we have $\frac{dx}{dt}=\frac{d}{dt}(t^{2}-2t)=2t - 2$.

Step3: Substitute $t = 2s$ into the velocity formula

When $t = 2$, $v=2\times2-2$.
$v = 2m/s$.

Answer:

$2m/s$