→ Initial velocity of the car = 108km/h
→ Final velocity of the car = 90km/h
→ Time taken = 5s
→ Displacement of the car in the last second of its motion, before it comes to halt.
Firstly, let's convert the initial and final velocity of the car from km/h to m/s.
=> 1km/h = 5/18m/s
=> 108km/h = 108×5/18
=> 30m/s (u)
=> 90km/h = 90×5/18
=> 25m/s (v)
Acceleration of the car :-
=> v = u + at
=> 25 = 30 + a(5)
=> -5 = 5a
=> a = -5/5
=> a = -1m/s²
Now, let's calculate the time taken(t') by the car to come to rest:-
=> 0 = 30 + (-1)t'
=> -30 = -t'
=> t' = 30s
Hence, the car comes to rest in 30 seconds.
So, displacement of the car in the 30th [last] second:-
=> Sₙₜₕ = u + a/2(2n - 1)
=> S₃₀ₜₕ = 30 + (-1/2)(2×30-1)
=> S₃₀ₜₕ = 30 + (-0.5)(59)
=> S₃₀ₜₕ = 30 - 29.5
=> S₃₀ₜₕ = 0.5m
Thus, displacement of the car in the last second of it's motion is 0.5m .
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
Given:-
→ Initial velocity of the car = 108km/h
→ Final velocity of the car = 90km/h
→ Time taken = 5s
To find:-
→ Displacement of the car in the last second of its motion, before it comes to halt.
Solution:-
Firstly, let's convert the initial and final velocity of the car from km/h to m/s.
=> 1km/h = 5/18m/s
=> 108km/h = 108×5/18
=> 30m/s (u)
=> 90km/h = 90×5/18
=> 25m/s (v)
Acceleration of the car :-
=> v = u + at
=> 25 = 30 + a(5)
=> -5 = 5a
=> a = -5/5
=> a = -1m/s²
Now, let's calculate the time taken(t') by the car to come to rest:-
=> 0 = 30 + (-1)t'
=> -30 = -t'
=> t' = 30s
Hence, the car comes to rest in 30 seconds.
So, displacement of the car in the 30th [last] second:-
=> Sₙₜₕ = u + a/2(2n - 1)
=> S₃₀ₜₕ = 30 + (-1/2)(2×30-1)
=> S₃₀ₜₕ = 30 + (-0.5)(59)
=> S₃₀ₜₕ = 30 - 29.5
=> S₃₀ₜₕ = 0.5m
Thus, displacement of the car in the last second of it's motion is 0.5m .