Question

On seeing a board of speed limit, a car decreases its speed from 90 km/h to 72 km/h at constant acceleration in 4 s. The acceleration of the car is
a) 1.25m/s2
b)-1.25m/s2
c)2.5m/s2
d)-2.5m/s2

Answer 1

Answer:

Explanation:

Given,

Initial velocity of the car, u = 90 km/h = 90 × 5/18 = 25 m/s

Final velocity of the car, v = 72 km/h = 72 × 5/18 = 20 m/s

Time taken by the car, t = 4 seconds

To Find,

Acceleration by the car, a

Formula to be used,

1st equation of the motion,

v = u + at

Solution,

Putting all the values, we get

v = u + at

⇒ 20 = 25 + a × 4

⇒ 20 - 25 = 4a

⇒ - 5 = 4a

⇒ - 5/4 = a

⇒ a = - 1.25 m/s².

Hence, the acceleration of the car is - 1.25 m/s².

Here, Option b, - 1.25 m/s² is correct answer.

Answer 2

$\large\underline{\sf{Given}}$

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» Initial velocity (u) of car = 90 km/h.

» Initial velocity (u) in m/s = 90 × 5/18 = 25 m/s.

» Final velocity (v) of car = 72 km/h.

» Final velocity (v) in m/s = 72 × 5/18 = 20 m/s.

» Time taken (t) by car to decrease it's speed = 4 s.

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$\large\underline{\sf{To\:Find}}$

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» Acceleration of car?

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$\large\underline{\sf{Solution}}$

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$\underbrace{\underline{\sf{\bigstar\:Understanding\:the\:Question\:::}}}$

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Here, we are given that on seeing a board of speed limit, a car decreases its speed from 90 km/h to 72 km/h at constant acceleration in 4 s. Henc, we have initial velocity, final velocity and time taken. We have to find the acceleration of car. We can easily find it by using first equation of motion :: v = u + at. In which, 'v' is final velocity, 'u' is initial velocity, 'a' is the acceleration and 't' is time taken. So, let's solve it!

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$\sf \longrightarrow\: v = u + at$

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Putting all known values,

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$\sf \longrightarrow\: 20 = 25 + a\big(4\big)$

$\\ \sf \longrightarrow\: 4a = 20 - 25$

$\\ \sf \longrightarrow\: 4a = -5$

$\\ \sf \longrightarrow\: a = {\cancel{\dfrac{-5}{4}}}$

$\\ \sf \longrightarrow\: \pink{Acceleration\:\big(a\big)\:of\:car = -1.25\:m/s^2}$

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$\therefore\:{\underline{\bf{Option\:\big(b\big)\:-1.25\:m/s^2\:\sf{is\:correct!}}}}$

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$\large\underline{\sf{More\:to\:know}}$

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Three equations of motion,

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• v = u + at ㅤㅤㅤㅤ[Used above]

• s = ut + ½ at²

• v² = u² + 2as

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Some important definitions,

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• Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change of velocity us considered as acceleration.

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• Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

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• Final velocity

After the effect of acceleration, the velocity of the object changes, the new velocity gained by the object is known as final velocity.

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