Question

A car travels initially at 15 m/s until it enters the highway. If the car accelerates at 10 m/s² for 84 meters, what is the new velocity?

a) 195 m/s

b) 105 m/s

c) 150 m/s

d) 135 m/s

Answer 1

The new velocity of the car is approximately 55.2 m/s.

Step-by-step explanation:

To find the new velocity of the car, we can use the equation:

v = u + at

Where:

• v is the final velocity
• u is the initial velocity
• a is the acceleration
• t is the time interval

Given that the initial velocity (u) of the car is 15 m/s and the acceleration (a) of the car is 10 m/s². The time interval can be found using the equation:

s = ut + 1/2at²

Where:

• s is the distance

Given that the distance (s) is 84 meters, we can rearrange the equation to solve for t:

t = sqrt(2s/a)

Substituting the given values:

t = sqrt(2(84)/10) = sqrt(16.8) ≈ 4.1 seconds

Now we can substitute the values into the velocity equation:

v = u + at = 15 + 10(4.1) = 55.2 m/s

Therefore, the new velocity of the car is approximately 55.2 m/s.