Question

A freight train travels with a velocity $\dot{x}=20(1-e^{-t})$m/s where t is the elapsed time in seconds. The distance travelled after 3 seconds is ______(m)

• A. 41

Answer 1

The correct option is A 41
$\text{velocity}\dot{x}=20(1-e^{-t})$

To find distance travelled

$\dot{x}=20(1-e^{-t})$

$\frac{dx}{dt}=20(1-e^{-t})$

$dx=20(1-e^{-t})dt$

Integrating both sides assuming no initial displacement

${\int }_0^{x}dx={\int }_0^{t}20(1-e^{-t})dt$

$x=20[t+e^{-t}{]}_0^t=20[t+e^{-t}-1]$

When t = 3 seconds

$x=20[3+e^{-3}-1]=40.996m$