Chapter 2, Problem 30P

To determine

To identify: Whether the driver of a carattempt to overtake truck or not.

Answer to Problem 30P

No, he shouldn’t attempt it.

Explanation of Solution

Given:

Initial velocity of car is $25\text{m/s}$ .

Constant acceleration of the car is $1.0{\text{m/s}}^{\text{2}}$ .

The total distance to overtake relatively to truck’s current position is $\left(20\text{m+10m+10m}\right)=40\text{m}$

Distance of the approaching car from the current position is $400\text{m}$ .

Formula used:

The speed-distance relationship is $s=\frac{d}{t}$ .

The second equation of motion is: $s=ut+\frac{a{t}^2}{2}$ .

Calculation:

Car will pass the truck when thedistance it is ahead is,

  $d\left(car\right)=d\left(truck\right)+40$  (1)

Relation of truck’s speed with the distance traveling is,

  $d\left(truck\right)=25t$  (2)

Now, using second equation of motion:

  $\begin{array}{l}d\left(car\right)=ut+\frac{a{t}^2}{2}\\ d(car)=25t+\frac{1\times t^2}{2}\end{array}$  (3)

Equate equation (1) and (3)

  $\begin{array}{l}d\left(car\right)=25t+40=25t+\frac{t^2}{2}\\ t^2=80\\ t=8.94\sec \end{array}$

Thus, car will overtake the truck in $8.94\sec$ and will have to cover distance,

  $d(car)=(25\times 8.94)+40=263.61\text{m}$

And, in the mean-time, the approaching car will pass this position in $(400-263.61)/25=5.46\sec$ .

This suggests that the car behind may collide with the approaching car. Thus, to save the accident, it is suggested to not to overtake the truck.

Conclusion:

Therefore, the car will not overtake truck.