We are given the following information about the automobile:

• Initial speed $u = 4.30 \, \text{m/s}$
• Acceleration $a = 3.00 \, \text{m/s}^2$
• Time $t = 5.00 \, \text{s}$

We can use the equations of motion to find both the final speed and displacement.

1. Final Speed

The formula for final speed under uniform acceleration is: $v = u + at$ Substitute the given values: $v = 4.30 \, \text{m/s} + (3.00 \, \text{m/s}^2)(5.00 \, \text{s})$ $v = 4.30 \, \text{m/s} + 15.00 \, \text{m/s}$ $v = 19.30 \, \text{m/s}$

2. Displacement

The formula for displacement is: $s = ut + \frac{1}{2}at^2$ Substitute the values: $s = (4.30 \, \text{m/s})(5.00 \, \text{s}) + \frac{1}{2}(3.00 \, \text{m/s}^2)(5.00 \, \text{s})^2$ $s = 21.50 \, \text{m} + \frac{1}{2}(3.00 \, \text{m/s}^2)(25.00 \, \text{s}^2)$ $s = 21.50 \, \text{m} + 37.50 \, \text{m}$ $s = 59.00 \, \text{m}$

Final Answers:

• Final Speed: $19.30 \, \text{m/s}$
• Displacement: $59.00 \, \text{m}$

Would you like more details, or do you have any questions?

5 related questions:

1. What is the effect of doubling the acceleration on final speed and displacement?
2. How would the displacement change if the initial speed were doubled?
3. How long would it take for the automobile to stop if it started with a speed of 19.30 m/s and decelerated uniformly at 3.00 m/s²?
4. How can we find the time required to reach a specific final speed given acceleration?
5. What is the relationship between acceleration and displacement when initial velocity is zero?

Tip:

When using the equations of motion, ensure the correct units (m/s, m/s², etc.) are used consistently throughout the calculations.