
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 25m/s .
Constant acceleration of the car is 1.0m/s2 .
The total distance to overtake relatively to truck’s current position is (20m+10m+10m)=40m
Distance of the approaching car from the current position is 400m .
Formula used:
The speed-distance relationship is s=dt .
The second equation of motion is: s=ut+at22 .
Calculation:
Car will pass the truck when thedistance it is ahead is,
d(car)=d(truck)+40 (1)
Relation of truck’s speed with the distance traveling is,
d(truck)=25t (2)
Now, using second equation of motion:
d(car)=ut+at22d(car)=25t+1×t22 (3)
Equate equation (1) and (3)
d(car)=25t+40=25t+t22t2=80t=8.94sec
Thus, car will overtake the truck in 8.94sec and will have to cover distance,
d(car)=(25×8.94)+40=263.61m
And, in the mean-time, the approaching car will pass this position in (400−263.61)/25=5.46sec .
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.
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