A Classical Approach of Newtonian Mechanics

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity

s

Worked example 2.2: Speed trap

Question: In a speed trap, two pressure-activated strips are placed 120 m apart on

a highway on which the speed limit is 85 km/h. A driver going 110 km/h notices

a police car just as he/she activates the first strip, and immediately slows down.

What deceleration is needed so that the car’s average speed is within the speed

limit when the car crosses the second strip?

Answer: Let v 1 = 110 km/h be the speed of the car at the first strip. Let ∆x =

120 m be the distance between the two strips, and let ∆t be the time taken by the

car to travel from one strip to the other. The average velocity of the car is

̄v =

∆x

.

∆t

We need this velocity to be 85 km/h. Hence, we require

∆t =

∆x

̄v

=

120

= 5.082.

85 × (1000/3600)

Here, we have changed units from km/h to m/s. Now, assuming that the accel-

eration a of the car is uniform, we have

∆x = v 1

which can be rearranged to give

∆t +

1

a (∆t)^2 ,

2

a =

2 (∆x − v 1 ∆t)

(∆t)^2

Hence, the required

deceleration is 2.73 m s−^2.

=

2 (120 − 110 ×

(1000/3600) × 5.082)

( 5. 0 8 2 )

(^2)