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Chapter 2: Q. 52 (page 62)

The minimum stopping distance for a car traveling at a speed

of 30 m/s is 60 m, including the distance traveled during the

driver鈥檚 reaction time of 0.50 s. What is the minimum stopping distance for the same car traveling at a speed of 40 m/s?

Short Answer

Expert verified

Minimum stopping distance travelled by the car at a speed of40m/sis100m.

Step by step solution

01

Given information

Speed of the car is u=30m/s.

Stopping distance of the car with this speed isD=60m.

Reaction time taken by the driver, t=0.50s.

02

Calculation of the distance travelled while deacceleration

During reaction time, the distance travelled by the driver is,

x=utx=30脳0.50mx=15m

Therefore, while slowing down, distance travelled by the driver is,

s=D-xs=60-15ms=45m

03

Calculation of stopping distance

Initial acceleration of the car can be calculated as,

0=u2+2asa=-u22sa=-3022脳45a=-10m/s2

Now, considering the initial speed as u'=40m/s,distance travelled by the car during constant motion is,

s1=u'ts1=40脳0.5ms1=20m

The distance travelled by the car during slowing down can be obtained as,

0=u'2+2as2s2=-u'22as2=-4022-10ms2=80m

Therefore, minimum stopping distance should be,

S=s1+s2S=20+80mS=100m

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