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Grade 11Trigonometry

The driver of a car moving at 30 m/s suddenly sees a truck moving in the same direction at 10m/s and is 60 m ahead. The maximum deceleration of the car is 5 m/s?.
a). Will the collision occur if the driver's reaction time is zero? If so, when?
B). If the car driver's reaction time of 0.5 sec included, what is the minimum deceleration required to avoid the collision.

Ushma

7 Years agoGrade 11

1 Answer

Aditya Gupta

Approved Tutor Answer7 Years ago

inital velocity of car=30m/s

a= – 5m/s^2

now, taking the truck to be at rest (concept of relative velocity),

we have inital velocity of car=30-10=20m/s

so the distance is related as :

2as=v^2-u^2, v=0, u=20, a= – 5

-10s=-400 or s=40 m, so the collision will not occur.

if the reaction time is 0.5 sec, then the car would have travelled 0.5*20=10m (note that we are once again taking the truck as a frame of reference)

so now the distance b/w car and truck is 60-10=50m

to find the minimum acceleration, we take s=50, v=0, and u=20

so we get 100a= 0 – 400

or a= – 4m/s^2

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