Question

A force $F$ is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of cart at $t=5sec$ is:

• A. $10m/s$
• B. $16.66m/s$
• C. $2m/s$
• D. Zero

Answer 1

The correct option is B $16.66m/s$

The equation of parabola is given as,

$P=k{t}^2$

$50=k{\left(5\right)}^2$

$k=2$

$P=2t^2$

The acceleration is given as,

$m{a}_x=2t^2$

$5\times a_x=2{\left(t\right)}^2$

$a_x=0.4{\left(t\right)}^2$

The velocity is given as,

$v=\underset{0}{\overset{t}{\int }}0.4t^2$

$v=0.4{\left[\frac{t^3}{3}\right]}_0^5$

$v=16.66m/s$