Question

The speed of a car as a function of time is shown in the figure. Find the distance traveled by car in $8$ seconds and its acceleration.

Answer 1

as, $a=\frac{dV}{dT}$

and also slope=$\frac{du}{dx}=\frac{dv}{dt}$

$\therefore$ slope=$a=\frac{10}{4}=\frac{20}{8}$

$\therefore a=\frac{5}{2}m/s^2$

Now, $S=ut+\frac{1}{2}a{t}^2$

$\therefore S=0+\frac{1}{2}\times \frac{5}{2}\times 64$

$S=80m$