Question

The acceleration produced the velocity of car increases from 30 km per hour 90 km per hour in 0.2 minute calculate the acceleration produced​? ​

Answer 1

Question:

• The velocity of car increases from 30 km per hour to 90 km per hour in 0.2 minute. Calculate the acceleration produced.

Answer:

• Acceleration produced by a car (a) is 1.38 m/s².

Step By Step Explanation:

Given that:

• Initial velocity of car (u) = 30 km/h
• Final velocity of car (v) = 90 km/h
• Time taken by car to increase it's velocity (t) = 0.2 min

To Find:

• Acceleration of car (a)?

Solution:

✭ How to solve :

• Here, we have initial velocity of car (u) = 30 km/h = (30 × 5/18) m/s = 8.33 m/s, final velocity of car (v) = 90 km/h = (90 × 5/18) m/s = 25 m/s and time taken by car (t) = 0.2 min = (0.2 × 60) sec = 12 sec. So, we will use first equation of motion to find acceleration of car (a).
• $\pmb{\boxed{\bf{\purple{v = u + at}}}}$
• Where, v denotes final velocity, u denotes initial velocity, a denotes acceleration and t denotes time taken.
• We have, v = 25 m/s, u = 8.33 m/s and t = 12 sec.

❏ Putting all known values :

↦ 25 = 8.33 + a(12)

↦ 25 - 8.33 = 12 × a

↦ 16.67 = 12a

↦ a = $\sf {\cancel{\dfrac{16.67}{12}}}$

➦ $\pmb{\blue{\underline{\boxed{\bf{\pink{a \approx 1.38\:{m/s}^{2}}}}}}}$

∴ Hence, acceleration produced by a car (a) is 1.38 m/s².

❏ Know More :

$\clubsuit$ Three equations of motion :

• v = u + at ㅤㅤㅤㅤㅤ[Used above]
• s = ut + ½ at²
• v² = u² + 2as

$\clubsuit$ Some important definitions :

• Acceleration

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

• Initial velocity

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

• Final velocity

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

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Answer 2

Answer:

$\green{ \boxed{\bf \bigstar\: \: \: \: acceleration \: \: a = 1.39 \: m {s}^{ - 2} }}$

Explanation:

Given,

$\bf \odot \: initial \: velocity \: \: u = 30 \: km {h}^{ - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{30 \times 1000}{3600} \: m {s}^{ - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8.33 \: m {s}^{ - 1} \\ \\ \bf \odot \: final \: velocity \: \: \: v \: = 90 \: km {h}^{ - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{90 \times 1000}{3600} \: m {s}^{ - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 25\: m {s}^{ - 1} \\ \\ \bf \odot \: \: time \: \: t \: =0.2 \: min \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.2 \times 60 \: \: s \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 12 \: s \\ \\ \green{ \bf \bigstar \: \: \:a cceleration \: \: \: a \: \: = \: to \: find} \\ \\ \bf \: we \: know \: that \: \\ \bf \: aceleration \: \: a = \frac{v - u}{t} \\ \\ \bf \implies \: \: a = \frac{25 -8 .33}{12} \\ \\ \bf \implies \: \: a = \frac{16.67}{12} \\ \\ \bf \implies \: \: a = 1.39 \: m {s}^{ - 2} \\ \\ \: \green{ \boxed{\bf \therefore\: \: \: \: acceleration \: \: a = 1.39 \: m {s}^{ - 2} }}$