Question

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

• A. 10m, 15 m/s
• B. 5m, 10 m/s
• C. 10m, 10 m/s
• D. 5m, 15 m/s

Answer 1

The correct option is B

5m, 10 m/s

W.r.t automobile
$u_{ta}=u_t-u_{a}att=0$
$=5m/s-0=5m/s$

$d_{ta}=dt-d_a$
$=0-10=-10m/s^2$

$\therefore s_{ta}=\left(u_{ta}\right)t+\frac{1}{2}\left(d_{ta}\right)t^2$
$=5\left(t\right)+\frac{1}{2}(-10)t^2$
When they over take, $s_{ta}=0$
$\therefore 0=5\left(t\right)-\frac{1}{2}{t}^2$
$\Rightarrow 0=5t-5t^2$
$\Rightarrow 5t(1-t)=0$
t=0,1

$\therefore$ They will overtake again at 1s
$\therefore v_t=5m/s\therefore s_t=v_t\times 1=5m$

$\therefore Att=1$, both truck and car would travelled 5m
Speed of autonobile,
v=u+at
=0 + 10(1)
=10 m/s