Question

A car is behind a truck going 25m/s on the highway. the car's driver looks for an opportunity to pass, guessing that his car can accelerate at 1.0m/s2. he gauges that he has to cover the 20m length of the truck, plus 10m clear room at the rear of the truck and 10m more at the front of it. in the oncoming lane, he sees a car approaching, probably also traveling at 25m/s. he estimates that the car is about 400m away. should he attempt to pass? give details.

Answer 1

Velocity of cars = 25 m/s

Distance the car has to cover for passing truck = 40m

Distance of passing spot from the car coming from opposite direction = 400- 40 =360 m

Time available for the car to pass truck of 20 m length = Distance of passing spot from the car coming from opposite direction/relative velocity between cars

Time = 360/50 = 7.2 seconds

Suppose the truck is moving at the same speed of car.

  Distance traveled by car compared to truck is given by the expression

                   S = ut + $\frac{1}{2} at^2$, where S is the distance traveled, u is the initial velocity a is the acceleration and t is the ime taken.

      In this case u = 0, t = 7.2 s, a = 1 m/$s^2$

So distance traveled by car in 7.2s compared to truck = 0*7.2+$\frac{1}{2} *1*7.2^2$

So,     S = 0+ 25.92 = 25.92 m

So car will travel only travel 25.92 m

In order to overtake it needs to travel 40m. So don't attempt to pass the truck.