Math Problem Statement

A car accelerates from rest at a constant rate of 3 m/s² for 8 seconds. Calculate the car's final velocity.

Solution

To calculate the car's final velocity, we can use the equation of motion:

v=u+atv = u + at

Where:

  • vv is the final velocity,
  • uu is the initial velocity,
  • aa is the acceleration,
  • tt is the time.

Given:

  • Initial velocity, u=0u = 0 m/s (since the car starts from rest),
  • Acceleration, a=3a = 3 m/s²,
  • Time, t=8t = 8 seconds.

Now, substituting the values into the equation:

v=0+(3m/s2)×8s=24m/sv = 0 + (3 \, \text{m/s}^2) \times 8 \, \text{s} = 24 \, \text{m/s}

So, the car's final velocity is 24 m/s.

Would you like any details or have any questions?

Here are 5 related questions to expand your understanding:

  1. What is the displacement of the car after 8 seconds?
  2. How would the final velocity change if the acceleration was doubled?
  3. What would be the final velocity if the car started with an initial velocity of 5 m/s?
  4. How would the time affect the final velocity if acceleration remained constant?
  5. What is the difference between constant and variable acceleration?

Tip: Always ensure the units are consistent when using equations of motion, especially in problems involving different physical quantities like time, velocity, and acceleration.