Question

Cell Phone Fight You are arguing over a cell phone while trailing an unmarked police car by 30 m. Both your car and the police car are traveling at 105 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 2.0 s, the police officer begins emergency braking at 5 m/s2. (a) What is the separation between the two cars when your attention finally returns? m (b) Suppose that you take another 0.4 s to realize your danger and begin braking. If you too brake at 5 m/s2, what is your speed when you hit the police car? km/h

Answer 1

(a)

Distance traveled by police car = ut+1/2 at²

Distance traveled by your car =ut

Difference = 1/2 at²

= -1/2 * 5 *2²

=- 10m

Therefore distance between them is reduced by 10m.

Therefore distance between them = 30-10=20m

(b)

At 2.4 s the distance between them is further reduced

Let the time at which they hit be t sec after the police car starts deceleration.

Distance traveled by ur car should be 30 m more than the police car to hit it.

Distance by police car(s₁)= ut+1/2at²

Distance by your car(s₂)

= 2.4u + u(t-2.4)+1/2 a(t-2.4)²

=[ut+1/2 at²] +2.88a - 2.4at

s₂-s₁ =30

2.88a-2.4at= 30

-14.4 + 12t =30

t=44.4/12 = 3.7 s

Time of deceleration = 3.7-2.4= 1.3 s

Velocity at time of collision = u+at

= 29.167 - 5*1.3

= 29.167-6.5

= 22.667 m/s or 81.56 km/hr