Question

A scooter is moving with a velocity of 20m/s when brakes are applied. The mass of the scooter and the rider is 180 kg. The constant force applied by the brakes is 500 N. (a) How long should be brakes be applied to make the scooter come to a halt ? (b) How far does the scooter travel before it comes to rest

Answer 1

Answer:

Explanation:

Solution,

Here, we have

Initial velocity, u = 20 m/s

Mass of scooter including, m = 180 kg

Force applied, F = 500 N.

Final velocity, v = 0 (As scooter stops)

To Find,

a. Time taken to stop, t = ?

b. Distance covered, s = ?

At 1st we will find out acceleration, a

We know that,

F = ma

a = F/m

So, putting all the values, we get

⇒ a = F/m

⇒ a = 500/180

⇒ a = 25/9 m/s.

Therefore, the acceleration is 25/9 m/s.

Now, we will find (a) time taken, t

According to 1st law of motion,

We know that,

v = u + at

So, putting all the values, again we get

v = u + at

⇒ 0 = 20 + (25/9) × t

⇒ 20 = 25/9t

⇒ 20 × 9/25 = t

⇒ 180/25 = t

⇒ t = 7.2 seconds

Hence, the time taken by scooter to halt is 7.2 seconds

Now, we will find (b) distance covered, s

According to 3rd law of motion,

We know that,

v² - u² = 2as

So, putting all the values, again we get

⇒ (0)² - (20)² = 2 × (25/9) × s

⇒ 400 = 2 × 25/9 × s

⇒ 200 = 25/9 × s

⇒ 200 × 9/25 = s

⇒ 1800/25 = s

⇒ s = 72 m.

Hence, the distance covered by scooter is 72 m.