Question

The acceleration of a given particle is given by $a\left(t\right)=e^{t/2}-1$, where $v_0=2m/s$ and $x_0=1m$.
How much time does it take for the particle to reach $x=50m$?

• A. $3.8s$
• B. $4.0s$
• C. $5.6s$
• D. $5.7s$
• E. $9.1s$

Answer 1

The correct option is D $5.7s$

$a=e^{t/2}-1=\frac{dv}{dt}$

$⟹v=2e^{t/2}-t+c$

$v_0=2=2+c$

$⟹c=0$

$v=2e^{t/2}-t=\frac{dx}{dt}$

$⟹x=4e^{t/2}-\frac{t^2}{2}+d$

$⟹x_0=1=4+d$

$⟹d=-3$

Hence $x=4e^{t/2}-\frac{t^2}{2}-3$

$⟹t=5.7s$ at $x=50$