Question

A motor care is travelling at 30 kmph. After 10 s the velocity becomes 60 kmph. Assuming the velocity change took place at a uniform rate find the acceleration.

Answer 1

✬ Acceleration = 0.834 m/s² ✬

Step-by-step explanation:

Given:

• A motor car is travelling at (u) = 30 km/h
• Final velocity (v) of motor = 60 km/h
• Time (t) taken to attain final velocity = 10 seconds.

To Find:

• What is the acceleration (a) of car ?

Formula to be used:

• v = u + at

Solution: Here, Unit of time is given in Second & speed is in Km/h. Therefore, we have to make the units same.

➛ For changing km/h to m/s we multiply by 5/18.

➮ Initial Velocity = (30 $\times$ 5/18)

➮ u = (150/18) = 8.33 m/s

➮ Final Velocity = (60 $\times$ 5/18)

➮ v = (300/18) = 16.67 m/s

Now Put the values on formula.

$\implies{\rm }$ v = u + at

$\implies{\rm }$ 16.67 = 8.33 + a $\times$ 10

$\implies{\rm }$ 16.67 – 8.33 = 10a

$\implies{\rm }$ 8.34 = 10a

$\implies{\rm }$ 8.34/10 = a

$\implies{\rm }$ 0.834 m/s² = a

Hence, the acceleration produced by the car is 0.834 m/s².

Answer 2

GIVEN:

• Initial Velocity (u) of the car = 30 km/hr
• Final velocity (v) of the car = 60 km/hr
• Time taken (t) by the car = 10 seconds

TO FIND:

• What is the acceleration of the car ?

SOLUTION:

We have given that, the initial Velocity and final velocity of the car is 30 km/hr and 60 km/hr respectively.

Convert km/hr into m/s:-

➟ $\rm{ u = 30 \: km/hr}$

➟ $\rm{ u = \cancel{30} \times \dfrac{5}{\cancel{18}}}$

➟ $\bf{ u = 8.33 \: m/s }$

➟ $\rm{ v = 60 \: km/hr}$

➟ $\rm{ v = \cancel{60} \times \dfrac{5}{\cancel{18}}}$

➟ $\bf{ v = 16.66 \: m/s}$

We know that the formula for finding the acceleration is:-

$\bf{\star \: Acceleration = \dfrac{Final \: Velocity - Initial \: Velocity}{Time\: Taken} \: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow Acceleration = \dfrac{ 16.66 - 8.33}{10}}$

$\rm{\dashrightarrow Acceleration = \cancel\dfrac{8.33}{10}}$

$\bf{\dashrightarrow \star \: Acceleration= 0.833 \: m/s^2 \: (approx)\: \star}$

❝ Hence, the acceleration of the car is 0.833 m/s² (approx) ❞

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