# A particle of mass 1 kg is moving with a variable speed, kt , where k = 1 m/s^2. Find mean kinetic energy from t = 1 s to t = 2 s.

Q: A particle of mass 1 kg is moving with a variable speed, kt , where k = 1 m/s2. Find mean kinetic energy from t = 1 s to t = 2 s.

(a) 1 J

(b) 7/6 J

(c) 6/7 J

(d) 9/11 J

Ans: (b)

Mean K.E , $\displaystyle K.E_m = \frac{\int_{1}^{2}K.E dt}{\int_{1}^{2}dt}$

$\displaystyle K.E_m = \frac{\int_{1}^{2}\frac{1}{2}m v^2 dt}{\int_{1}^{2}dt}$

$\displaystyle K.E_m = \frac{\int_{1}^{2}\frac{1}{2}m (kt)^2 dt}{\int_{1}^{2}dt}$

$\displaystyle K.E_m = \frac{\frac{1}{2}m k^2\int_{1}^{2}t^2 dt}{\int_{1}^{2}dt}$