Question

A body is moving with velocity $30\text{m/s}$. A variable force $a\text{N}$ is applied at $t=0\text{s}$ on the body such that it increases it's velocity to $90\text{m/s}$ at $t=4\text{s}$ in same direction. The variation of force with time is shown in graph.

If mass of body is $10kg$, find the value of $a$ (shown in graph)

• A. $150\text{N}$
• B. $100\text{N}$
• C. $50\text{N}$
• D. $125\text{N}$

Answer 1

The correct option is A $150\text{N}$


We know
Impulse imparted by force for $(t=0)\text{s}\text{to}(t=4)\text{s}=$ {area under (F-t) graph from $(t=0\text{s})\text{to}(t=4\text{s})$}
Also impulse imparted by force $=\Delta mv$
$\Rightarrow a\times 4=m\Delta v$
$4a=10\times [90-30]$
$4a=10\times 60$
$a=150\text{N}$