Question

A car accelerates at a constant rate from 15 m/s to 25 m/s while it travels a distance of 125 m. How long does it take to

achieve the final speed?

Answer 1

So, it takes 6.25 seconds to achieve the final speed.

Introduction

Hi ! Here I will help you to discuss material about accelerated uniform change in straight motion. In uniformly accelerated motion, it will always refer to the relationship between time, initial velocity, final velocity, acceleration, and the distance. To reach any speed (the value is always higher if you do acceleration), the value of the constant acceleration will affect the time. Then, the time will also affect the distance traveled.

Formula Used

To solve this problem, there are two formula that you should know.

Relationship Between Acceleration, Distance, and Initial-Final Velocity

`\boxed{\sf{\bold{(v_t)^2 = (v_0)^2 + 2 \cdot a \cdot s}}}`

With the following condition :

• 
  `\sf{v_t}` = final velocity respect to the time (m/s)
• 
  `\sf{v_0}` = initial velocity (m/s)
• a = acceleration that happen (m/s²)
• s = shift or distance (m)

Relationship Between Acceleration, Time, and Initial-Final Velocity

`\boxed{\sf{\bold{a = (v_t -v_0)/(t)}}}`

With the following condition :

• a = acceleration that happen (m/s²)
• 
  `\sf{v_t}` = final velocity respect to the time (m/s)
• 
  `\sf{v_0}` = initial velocity (m/s)
• t = time (s)

Problem Solving

We know that :

• 
  `\sf{v_t}` = final velocity respect to the time = 25 m/s
• 
  `\sf{v_0}` = initial velocity = 15 m/s
• s = shift or distance = 125 m

What was asked ?

• t = time = ... s

Step by step :

• Calculate the value of acceleration.

`\sf{(v_t)^2 = (v_0)^2 + 2 \cdot a \cdot s}`

`\sf{(25)^2 = (15)^2 + 2 \cdot a \cdot 125}`

`\sf{625 = 225 + 250 \cdot a}`

`\sf{250 \cdot a = 625-225}`

`\sf{250 \cdot a = 400}`

`\sf{a = (400)/(225)}`

`\sf{\bold{a = 1.6 \: m/s^2}}`

• Calculate the time that needed

`\sf{a = (v_t -v_0)/(t)}`

`\sf{1,6 = (25 -15)/(t)}`

`\sf{1,6 \cdot t = 10}`

`\sf{t = (10)/(1,6)}`

`\boxed{\sf{t = 6.25 \: s}}`

Conclusion:

So, it takes 6.25 seconds to achieve the final speed.