Question 3. 6. A car moving along a straight highway with speed of 126 km h-1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?
Answers
Answer :
the time taken by the car = 11.4s
Given :-
Distance covered by the car before coming to rest = 200 m
A car moving along a straight highway with speed = 126 km h⁻¹
To Find :-
Time taken for the car to stop.
Analysis :-
First, using the third equation of motion, find the acceleration.
Using the first equation of motion substituting the value given in the question accordingly considering the time as a variable.
Solution :-
We know that,
- v = Final velocity
- a = Acceleration
- u = Initial velocity
- t = Time
- s = Distance
By the third equation of motion,
Given that,
Initial velocity (u) = 126 km/h = 35 m/s
Distance travelled (s) = 200 m
Final velocity (v) = 0 (Since the car comes under rest)
Substituting their values,
a = (v² - u²)/2s
a = (0 - 35)/2×200
a = -1225/400
a = -3.06 m/s²
Therefore, the acceleration is -3.06 m/s².
Let the time be 't'.
Using first equation of motion,
Given that,
Initial velocity (u) = 126 km/h = 35 m/s
Distance travelled (s) = 200 m
Final velocity (v) = 0
Acceleration = -3.06 m/s²
Substituting their values,
0 = 35 - 3.06 × t
t = 35/3.06
t = 11.43 sec
Therefore, it takes 11.43 sec for the car to stop.