Question

A body moving with uniform retardation covers 3 km before its speed is reduced to half of its initial value, it comes to rest in another distance of
1- 1 km
2- 2 km
3- 3 km
4- 0.5 km

Answer 1

Here it is mentioned retardation. Retardation is negative acceleration. When a body moves with constant acceleration, then there is a uniform change in its speed.

Complete Step by step answer:
Given, Acceleration, a = -3 $m/{{s}^{2}}$
Distance covered, s= 3 km
Let initial velocity be 2u then its final velocity will be u. Using third equation of motion we get,

$$\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\\ \Rightarrow {{u}^{2}}-4{{u}^{2}}=6a \\\$$

$\Rightarrow -3{{u}^{2}}=6a$
$\Rightarrow a=-0.5{{u}^{2}}$--(1)
Now initial velocity is u and final velocity is 0, let distance covered is m km

$$\Rightarrow {{v}^{2}}-{{u}^{2}}=2as \\\ \Rightarrow 0-{{u}^{2}}=2ma \\\ \Rightarrow -{{u}^{2}}=2ma \\\$$

Using (1), we get, $2a=2ma$
$\Rightarrow m=1$ km

So, the correct option is (1).

Additional information: Acceleration time graph does not give us velocity or position; it is only telling us acceleration. If the acceleration time graph is a line parallel to the x-axis it does not mean that the body is at rest but it means the body is moving with constant acceleration.

Note: A positive value of acceleration means the speed of the body is increasing while the negative value of acceleration means the velocity of the body is decreasing. Negative acceleration also termed as retardation. If a body moves with constant velocity then acceleration produced in the body is zero.