Question

A body starts from rest and is acted on by a constant force. The ratio of kinetic energy gained by it in the first five seconds to that gained in the next five second is:

• A. $2:1$
• B. $1:1$
• C. $3:1$
• D. $1:3$

Answer 1

The correct option is D $1:3$

1) constant force $\to$ constant acceleration $=a$

$\Rightarrow \frac{V_5-v_0}{t}=a=\frac{v_5-0}{5}=a\Rightarrow V_5=5a$

$\Rightarrow K{E}_5=\frac{1}{2}m{v}_5^2=\frac{25}{2}m{a}^2$

2) $\frac{v_{10}-v_0}{t}=a\Rightarrow v_{10}=10a\Rightarrow K{E}_{10}=\frac{100}{2}m{a}^2$

So $KE$ gained between $5s$ and $10s$ $=K{E}_{10}-K{E}_5$
$=\frac{75}{2}m{a}^2$

$KE$ gained in $5s$$=\frac{25}{2}m{a}^2$

$\Rightarrow Ratio=\frac{25}{75}=1:3$