Question

The graph of acceleration - time of a particle moving in straight path makes angle 45° with time axis.
It start from rest. Then distance travelled by it in first 6 sec is
(1) 36 m
(2) 216 m
(3) 18 m
(4) 72 m​

Answer 1

Answer:

Option (1) 36 m

Explanation:

The fuction for acceleration a, if the time is t, will be

a = t

or, dv/dt =t

or $dv=tdt$

$\implies \int dv=\int tdt$

$\implies v=\frac{t^2}{2}+C$   where C is a constant

At time t=0, v = 0

Therefore C = 0

$\implies v=\frac{t^2}{2}$

Now, $v=\frac{t^2}{2}$

or, $ds/dt=t^2/2$

$\implies dsx=(t^2/2)dt$

$\implies \int_0^s ds= \int_0^{6} (t^2/2)dt$

$\implies s=\frac{t^3}{6}\Bigr|_0^{6}$

$\implies s=\frac{6\times 6\times 6}{6}$

$\implies s=36$

Therefore, the distance travelled in 6 seconds is 36 m