A scooter moving at a speed of 10 m/s is stoped by applying brakes which produce a uniform acceleration of-0.5m/s.how much distance will be covered by a scooter
Answers
Solution:
Given,
- Speed of scooter = 10 m/s
- Stopped by applying brakes produces uniform acceleration of -0.5 m/s²
To find ,
- Distance covered
_____________________________
Here ,
Initial velocity = 10 m/s
Final velocity = 0 m/s because the scooter is stopped by applying brakes.
Acceleration = - 0.5 m/s²
Note : Negative symbol in Acceleration indicates deceleration
Using the 3rd equation of motion
v² - u² = 2as
Where
- v : final velocity
- u : initial velocity
- a : acceleration
- s : distance
→ 0² - 10² = 2(-0.5)(s)
→ 0 - 100 = 2 × (-1/2) × s
→ - 100 = - s
→ s = 100 m
Hence , distance covered = 100 m
Answer:
s = a/2 * t² + v(0) * t
s = -0,25 m/s² * t² + 10m/s * t
v = ds/dt = a * t + v(0) = -0,5 * t + 10 m/s
when scooter stopped due to braking we have
v= 0 = -0,5 * t + 10 m/s = 0
t=10m/s/(0,5 m/s²) = 20 seconds
then using
s = -0,25 m/s² * t² + 10m/s * t
you will find out that after 20 seconds you covered a maximum distance of 100 m
s(20s) = -0,25 m/s² * 400s² + 10m/s * 20s = -100 m+ 200m = 100 m