Question

The motion of a particle is described by the equation $u=at$. The distance travelled by particle in first $4$s is

• A. $4a$
• B. $12a$
• C. $6a$
• D. $8a$

Answer 1

The correct option is D $8a$

Equation of motion is $u=at$

we know that $u=\frac{ds}{dt}\Rightarrow \frac{ds}{dt}=at$ or $ds=atdt$

integrating it we get,

${\int }_0^{s}ds=a{\int }_0^{4}tdt$

$s=\frac{a}{2}{\left[t^2\right]}_0^4=8a$