a body moving with 40 m/s is uniformly retarded to a velocity 20m/s by travelling a distance of 100 m find retardation and time taken to travel the distance
Answers
Given :-
Initial Velocity of body = u = 40 ms-¹
Final Velocity of body = v = 20 ms-¹
Distance travelled = S = 100 m
To find :-
1. Acceleration.
2. Time taken to travel the distance.
Solution :-
Using third equation of motion we will find the acceleration of body.
v² - u² = 2aS
(20)² - (40)² = 2×a×100
400- 1600 = 200a
a = -1200/200
a = -6 ms-²
After finding acceleration we will find the time taken :-
Using second equation of Motion.
S = ut + 1/2 at²
100 = 40t + 1/2 × (-6)t²
3t² - 40t + 100 = 0
3t² - 30t - 10t + 100 = 0
3t(t - 10) - 10(t - 10) = 0
(3t - 10)(t - 10) = 0
If product of two terms is equal to zero then either first term is equal to zero or second term is equal to zero.
3t - 10 = 0
t = 10/3 s
or
t - 10 = 0
t = 10 s
Therefore,
Time taken = t = 10/3s , 10s