Question

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

Answer 1

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 2

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