Question

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

Answer 1

Hint
It is common to use acceleration to mean speeding up and the word deceleration to mean slowing down. Strictly speaking, however, acceleration describes both types of motion. Speeding up might be referred to as positive acceleration and slowing down as negative acceleration .

Complete step by step answer
The distance formula is $ s = ut + \dfrac{1}{2}a{t^2} $ … (1)
Now, For the case 1.
Distance $s = 200, time t = 2 sec$,
So according to the equation (1)
$ 200 = 2u + 2a $
$ u + a = 100 $ ...equation (2)
For case 2 i.e. next 4 seconds, we have distance = 420 cm and time = 6 s
$ 420 = 6u + 18a $
$ u + 3a = 70 $ .... equation (3)
Solving equation 2 and 3, we get,
$
(3a + u) - (a + u) = 70 - 100 \\
2a = - 30 \\
  \therefore a = - 15 \\
  $
Now, after putting the value of $a$ in to the equation 1 we get,
$ u = 100 + 15 = 115cm/s $
$u=115 cm/s and a=−15 cm/s^2$
Now, according to the velocity formula we get,
$ \begin{array}{*{20}{l}}
  {v = u + at} \\
  { \Rightarrow v = 115 - 15 \times 7} \\
  { \Rightarrow v = 10{\text{ }}cm/s}
\end{array} $.

Note
Velocity describes the motion of objects. Velocity measures the movement of objects based on their speed and direction. Speed is a scalar measurement since it only defines the magnitude of how fast an object is moving. Velocity is a vector quantity since it describes both speed and direction.