A car moving with certain velocity comes to halt after covering a distance of 62.5m if reatardation was 5m/s2 find the initial velocity of the car
Answers
Concept:
Equations of motion:
1) v = u + at
2) s = ut + 1/2 at²
3) v² - u² = 2as
where v = Final velocity of the object
u = Initial velocity of the object
a = Acceleration of the object
t = Time taken
s = Distance covered
Given:
Distance covered by the car, s = 62.5 m
Acceleration, a = -5 m/s² [-ve sign signifies the retardation (decrease in velocity)
Final velocity, v = 0 m/s [As car comes to halt means it stops.]
Find:
Initial velocity of the car.
Answer:
Initial velocity of the car is 25 m/s.
Solution:
As we are given only distance, final velocity and acceleration, we will use the third equation of motion for finding the initial velocity of the car.
Let the initial velocity of the car be u.
According to the third equation of motion, we have,
v² - u² = 2as --------------------------- (i)
s = 62.5 m
a = -5 m/s²
v = 0 m/s
Putting the values in (i), we get
(0)² - u² = 2(-5)(62.5)
-u² = -625
u² = 625
u = √625
u = 25 m/s
Hence, the initial velocity of the car is u = 25 m/s.
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