Question

A body travels 200 cm in the first 2 seconds and 220 cm in next 4 seconds. What will be the velocity at the end of the 7th second of the start?

A. 2 cm/s

B. 8 cm/s

C. 10 cm/s

D. 15 cm/s

Answer 1

Hint: First of all, find the initial velocity and acceleration of the body by using the second equation of motion. Then find the velocity at 7th sec by using the first equation of motion and the obtained values of initial velocity and the acceleration of the body. 

Formulae used: \[s = ut + \dfrac{1}{2}a{t^2}\], \[v = u + at\]

Given at time \[t = 2{\text{ sec}}\], distance covered by the body \[s = 200{\text{ cm}}\]

Complete step-by-step solution -

We know the formulae for second equation of motion i.e., \[s = ut + \dfrac{1}{2}a{t^2}\] where \[s\] is the distance covered, \[u\] is the initial speed of the body, \[t\] is the time taken and \[a\] is the acceleration of the body. So, at time \[t = 2{\text{ sec}}\] and \[s = 200{\text{ cm}}\], we have

$200 = u\left( 2 \right) + \dfrac{1}{2}a{\left( 2 \right)^2}$

$\Rightarrow 200 = 2u + 2a $

$\Rightarrow 100 = u + a $

$\Rightarrow u = 100 - a........................................................................\left( 1 \right) $

Also, the body covers a distance of 220 cm in the next 4 sec.So, we have \[t = 2 + 4 = 6{\text{ sec}}\] and \[s = 200 + 220 = 420\], we have

$ 420 = u\left( 6 \right) + \dfrac{1}{2}a{\left( 6 \right)^2} $

$\Rightarrow 420 = 6u + 18a $

$\Rightarrow 70 = u + 3a $

$\Rightarrow u = 70 - 3a..............................................................\left( 2 \right)$

From equation (1) and (2), we have

$100 - a = 70 - 3a $

$\Rightarrow 3a - a = 70 - 100 $

$\Rightarrow 2a =  - 30 $

$\Rightarrow  a =  - 15{\text{ cm/}}{{\text{s}}^2}$

By substituting \[a =  - 15\] in equation (1) we get

$u = 100 - \left( { - 15} \right) = 100 + 15 $

$\Rightarrow  u = 115{\text{ cm/s}} $

From the equations of motion, we know that \[v = u + at\] where \[v\] is the final velocity of the body, \[u\] is the initial velocity of the body, \[a\] is the acceleration of the body and \[t\] is the time taken by the body to cover a particular distance. 

So, the velocity at the end of 7th second i.e., at \[t = 7{\text{ sec}}\], we have

$\Rightarrow v = 115 + \left( { - 15} \right)7 $

$\Rightarrow v = 115 - 105 $

$\therefore v = 10{\text{ cm/s}} $

Thus, the correct option is C. 10 cm/s.

Note:  Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. Generally, we have three equations of motion which are also known as the laws of constant acceleration in the case of uniform acceleration.