A body covers 200 cm in the first 2 seconds and 220 cm in the next 4 seconds. The velocity of the body at the end of the $7^{th}$ second is
Updated On: Jul 5, 2022
$10 \,cm \,s^{-1}$
$20 \,cm \,s^{-1}$
$5 \,cm \,s^{-1}$
$30 \,cm \,s^{-1}$
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The Correct Option isA
Solution and Explanation
Let u and a be the initial velocity and uniform acceleration of the body.
Using $ S = ut + \frac{1}{2}at^{2}$$\therefore\quad 200 = u\left(2\right) + \frac{1}{2}a\left(2\right)^{2}$$100 = u + a\quad ...\left(i\right)$
Also $420 = 6u +\frac{1}{2}a\left(6\right)^{2}$$70 = u + 3a \quad...\left(ii\right)$
Solving equations $\left(i\right)$ and $\left(ii\right)$, we get
$u = 115\, cm\, s^{-1}, a = - 15\, cm \,s^{-2}$
Using $\upsilon = u + at$$\therefore\quad\upsilon = 115 + \left(-15\right)7 = 10 \,cm\, s^{-1}$
The motion in a straight lineis 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.
