A car and a truck are going on a straight road each having a velocity of 72 km/h. The car cannot come to a stop in less than 3.0 sec and the truck takes 5.0 seconds time to stop on the high-way. The car is behind the truck. The truck gives a signal for stopping at a tollplaza. What should be the least distance of the car from the truck so that it does not bump onto the truck? (Take human response time to be 0.5 sec)

Options

A. 1.25 m
B. 0.75 m
C. 1.5 m
D. 1.75 m

Answer

a

Explanation

Here can is moving behind the truck . Now retardations of the truck and car be `a_1` and `a_c`
Then `a_t=(20)/(5)=4 ms^(-2)`
and `a_c=(20)/(3) ms ^(-2)`
Applyings v=u+at
For truck `v_t=20-4t`
`=-(1)/(2)xx(20)/(3)[(5)/(4)-0.5]^(2)`
`S_(c)`=23.125 m
Thus `S_(c)-S_(t)`=1.25 m.
Hence the speed of the car will always be less than the truck and they will never collide if they maintain these speeds