Question

A car accelerates uniformly from rest to a speed of 20 m/s in 8 seconds. What is the distance covered by the car during this time?

• A. 80 m
• B. 160 m
• C. 100 m
• D. 120 m

Hint:

For uniform acceleration, use the equation \( s = ut + \frac{1}{2} a t^2 \) to find distance, ensuring all units are consistent.

Answer 1

The Correct Option is A

Given: \[ u = 0 \, \text{m/s}, \quad v = 20 \, \text{m/s}, \quad t = 8 \, \text{s} \] Step 1: Calculate Acceleration
Use the first equation of motion: \[ v = u + at \implies 20 = 0 + a \cdot 8 \implies a = \frac{20}{8} = 2.5 \, \text{m/s}^2 \] Step 2: Calculate Distance
Use the second equation of motion: \[ s = ut + \frac{1}{2} a t^2 \] Substitute the values: \[ s = 0 \cdot 8 + \frac{1}{2} \cdot 2.5 \cdot (8)^2 = 0 + \frac{1}{2} \cdot 2.5 \cdot 64 = 1.25 \cdot 64 = 80 \, \text{m} \] Thus, the distance covered is: \[ \boxed{80 \, \text{m}} \]