NEET Practice Questions (MCQs) with Answers & Solutions

From Example 2.7, an object under free fall (like the ruler) starts with an initial velocity $v_0 = 0$. The distance travelled ($d$) is related to time ($t_r$) by the kinematic equation $d = v_0 t_r + \frac{1}{2} a t_r^2$. Since $v_0 = 0$ and acceleration $a = g$, the equation simplifies to $d = \frac{1}{2} g t_r^2$. Note: The solution in the text uses $a = -g$ when defining the direction of motion relative to the coordinate system, but for the magnitude of distance traveled downwards, 'g' is used positively.

During the reaction time, the car continues to move at its initial speed before deceleration begins. The distance covered during reaction time can be calculated as distance = speed × time. So, distance = $20 \text{ m/s} \times 0.5 \text{ s} = 10 \text{ m}$.

Example 2.7 states, 'Reaction time depends on complexity of the situation and on an individual.' Therefore, the complexity of the situation directly influences reaction time.

The stopping distance formula is $d_s = \frac{-v_0^2}{2a}$. Here, '$a$' represents deceleration, which is inherently negative. If we consider the magnitude of deceleration, a larger magnitude of 'a' (meaning stronger braking) would lead to a smaller stopping distance because 'a' is in the denominator. The faster you can decelerate, the shorter the distance needed to stop.

The text explicitly states, 'Stopping distance is an important factor considered in setting speed limits, for example, in school zones.' This is because school zones have a higher risk of unexpected pedestrian (children) presence, necessitating shorter stopping distances at lower speeds to prevent accidents.

The context states: 'If in a population of size N, the birth rates (not total number but per capita births) are represented as b and death rates (again, per capita death rates) as d, then the increase or decrease in N during a unit time period t (dN/dt) will be dN/dt = (b – d) × N. Let (b–d) = r, then dN/dt = rN.' This is the equation for exponential growth.

The context defines 'r' as: 'Let (b–d) = r'. Here, 'b' represents per capita birth rates and 'd' represents per capita death rates. Therefore, 'r' is the per capita birth rates minus the per capita death rates.

The context states: 'Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number... Then the population grows in an exponential or geometric fashion.' This clearly indicates that unlimited resources are essential for exponential growth.

The context mentions: 'The above equation describes the exponential or geometric growth pattern of a population (Figure 11.3) and results in a J-shaped curve when we plot N in relation to time.'

The context states: 'Since resources for growth for most animal populations are finite and become limiting sooner or later, the logistic growth model is considered a more realistic one.'