Question

Acar travels with a uniform velocity of $20m{s}^{-1}$ for 5 sec. The brakes are then applied and the car is uniformly retarded. It comes to rest in further 8 sec. by drawing a graph between velocity and time-find.

1. The distance traveled in the first 5 sec.
2. The distance traveled after the brakes are applied.
3. Total distance traveled.
4. Acceleration during the first 5 sec.
5. Acceleration during the last 8 sec.

Answer 1

Given, $u=20m/s$

$t_1=5s$

$t_2=8s$

Graph: (Refer to Image)

(1) Distance travelled in first $5$ sec= area of ABDE= $20\times s=80m$

(2) Distance travelled after the brakes are applied (area of BCD)= $\frac{1}{2}\times 8\times 5=20m$

(3) Total distance travelled= $AreaofABCDE+AreaofBCD=80+20=100m$

(4) Acceleration during the first $5$ sec= $0$, because uniform velocity.

(5) Acceleration during the last $8$ sec= $v=0,u=20m/s,t=8sec$

$\Rightarrow v=u+at\Rightarrow 0=20+a\left(8\right)$

$\Rightarrow a=-2.5m/s^2$ (slope of the line DC)