Question

a car is moving with a speed of 54 km /h comes to rest 2secondson applying brake ifthe mass of the car including the passengers is1000 kg what will be the force applied when brake is applied​

Answer 1

Answer:-

• Force applied on Car on applying brakes = -7500 N

Given:-

• Car is moving with a speed of 54 km/h
• On applying brake Car comes to rest after 2 seconds
• Mass of the Car including passenger is 1000 kg

To find:-

• Force applied when the brake is applied, F =?

Formula required:-

• The first equation of motion

         v = u + at

• The expression for newton's second law

        F = ma

[ Where v = final velocity, u = initial velocity, a = acceleration, t = time, F = force, m = mass ]

Solution:-

• Initial velocity of Car, u = 54 km/h = 54×5/18  m/s = 15 m/s
• Final velocity of Car, v = 0
• time taken for coming to rest, t = 2 s
• Mass of Car with passenger, m = 1000 kg

Let, the acceleration of car on applying brake be 'a'

Using the first equation of motion

→ v = u + at

→ 0 = 15 + a × 2

→ -15 = 2 a

→ a = -7.5 m/s²

Let, the force acted on applying brake be 'F'

Using Newton's second law

→ F = ma

→ F = 1000 × -7.5

→ F = -7500 N

Therefore,

• A force of 7500 N (In the opposite direction of motion of Car) acted on applying brakes.

Answer 2

${\bold{\sf{Question}}}$

A car is moving with a speed of 54 km/h comes to rest 2 seconds on applying brake if the mass of the car including the passengers is 1000 kg what will be the force applied when brake is applied ?

${\bold{\sf{Given \; that}}}$

✠ Speed = 54 km/h

✠ While applying brake car come in rest after 2 seconds.

✠ Mass of car including the passengers = 1000 kg

${\bold{\sf{To \; find}}}$

✠ Force applied when brake is applied.

${\bold{\sf{Solution}}}$

✠ Force applied when brake is applied = -7500 N

${\bold{\sf{Using \; concepts}}}$

✠ 1st equation of motion. (Newton's)

✠ 2nd equation of motion. (Newton's)

${\bold{\sf{Using \; formula}}}$

✠ 1st equation of motion = v = u + at

✠ 2nd equation of motion = F = ma

${\bold{\sf{We \; also \; write \; these \; as}}}$

✠ Final velocity as v.

✠ Initial velocity as u

✠ Acceleration as a

✠ Time as t

✠ Mass as m

✠ Force as F

${\bold{\sf{Understanding \: the \: question}}}$

✠ This question says that there is a car which is moving with a speed of 54 km/h afterthat while applying brake car come in rest after 2 seconds. Then the question says that the mass of car including passengers is 1000 kg . What will be the force applied when brake is applied ? Means it's cleared that what the concept says!

${\bold{\sf{Procedure}}}$

✠ To solve this problem 1stly we have to convert km/h into m/s afterthat we have to take a view on final velocity, initial velocity or something else to under the concept more clearly. Now we have to use Newton's first law of motion formula 1stluly applying it we get -7.5 m/s² as acceleration. Afterwards putting the values according to Newton's 2nd law of motion we get -7500 N as our final result. N denotes symbol of force !

${\bold{\sf{Full \; solution}}}$

✠ Final velocity = 0 m/s

✠ Initial velocity = 54 km/h = 15 m/s

✠ Mass of car including passengers = 1000 kg

✠ Time taken to coming at rest (applying brake) = 2 seconds

${\bold{\bf{Why \: final \: velocity \: become \: 0 \: m/s}}}$

It's become 0 m/s because of a very simple reason and the reason is that the car take a rest means it's given in question that the car is at a rest while applying a brake and it's already known to us that when an object take a rest then it's velocity be 0.

${\bold{\sf{Coming \: to \: question}}}$

Using 1st law of motion we get

⇝ v = u + at

↦ 0 = 15 + a × 2

↦ -15 = 2a

↦ a = -15 / 2

↦ a = -7.5 m/s²

Now using 2nd law of motion we get

⇝ F = ma

↦ F = 1000 × -7.5

↦ F = -7500 N

Henceforth, force applied when brake is applied = -7500 N