A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

To determine the acceleration of the car, we can use the kinematic equation for motion with constant acceleration: \[ d = v_0 t + \frac{1}{2} a t^2 \] where: - \(d\) is the distance traveled (110 m), - \(v_0\) is the initial velocity (0 m/s, since the car starts from rest), - \(t\) is the time (5.21 s), - \(a\) is the acceleration (which we want to find). Since the initial velocity \(v_0\) is 0, the equation simplifies to: \[ d = \frac{1}{2} a t^2 \] Substituting the values into the equation: \[ 110 = \frac{1}{2} a (5.21)^2 \] Calculating \( (5.21)^2 \): \[ (5.21)^2 = 27.1441 \] Now we can insert this back into the equation: \[ 110 = \frac{1}{2} a \cdot 27.1441 \] Multiplying both sides by 2 to eliminate the fraction: \[ 220 = a \cdot 27.1441 \] Now, solve for \(a\): \[ a = \frac{220}{27.1441} \approx 8.11 \, \text{m/s}^2 \] Thus, the acceleration of the car is approximately \( \boxed{8.11 \, \text{m/s}^2} \).