Question

As a stunt for movie two cars are to collide with each other head on. The two cars are initially 125 apart. Car A is heading straight for car B at 30 m/s and car B is at rest. Car A maintain the same velocity, while car B accelerates toward car A at constant 4 m/s2.
(a) Find out the time when do the car collide
(b) Where do the cards collides?
(c) How fast the car B moving at the moment of collision?

Answer 1

Answer:

3.39724 seconds

23.0824792352 m, 101.917520765 m

13.58896 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

The equation of motion will be

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow 125=30\times t+\dfrac{1}{2}\times 4\times t^2\\\Rightarrow 2t^2+30t-125=0\ m$

$t=\frac{5\left(\sqrt{19}-3\right)}{2},\:t=-\frac{5\left(3+\sqrt{19}\right)}{2}\\\Rightarrow t=3.39724, -18.39724$

The time at which the cars collide is 3.39724 seconds

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 4\times 3.39724^2\\\Rightarrow s=23.0824792352\ m$

Car B traveled 23.0824792352 m and Car A traveled 125-23.0824792352 = 101.917520765 m

$v=u+at\\\Rightarrow v=0+4\times 3.39724\\\Rightarrow v=13.58896\ m/s$

The speed of car B is 13.58896 m/s