Question

A car moving at a speed of 8.0 m/s merges onto the highway and accelerates at a rate of

3.0 m/s2. How fast is it moving after travelling for 54 meters?

Answer 1

`\large\underline{\underline{\red{\sf \blue{\longmapsto} Step\:-\:by\:-\:step\: Explanation:-}}}`

As per the data in Question,

• Initial velocity of car = 8m/s (u)
• Final velocity of car = ? (v) .
• Acceleration of the car = 3.0m/s².
• Distance travelled by the car = 54m .

Using the third equation of motion :-

`\boxed{\red{\bf\purple{\dag}\:\:2as\:=\:v^2\:-\:u^2}}`

Substituting the respective values ,

⇒ 2as = v² - u² .

⇒ 2 × 3 × 54 = v² - 8²

⇒ 324 + 64 = v² .

⇒ v² = 388.

⇒ v = √388 .

⇒ v = 19.69 m/s ≈ 20m/s .

Hence the required answer is 19.69 m/s.