Question

A car drives down the highway at a certain speed. The speed limit increases, and the car accelerates to 33 m/s in 4.3 seconds over a displacement of 100 meters. What is the car's acceleration?

Answer 1

To determine the car's acceleration, we must first estimate the initial velocity using the displacement, final velocity, and time, then apply the kinematic equation to find the acceleration.

Step-by-step explanation:

To find the acceleration, we can use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. However, we are not given the initial velocity directly, but we can determine it using the other kinematic equation s = ut + (1/2)at², where s is the displacement. Solving for initial velocity (u). Let's rearrange the second equation to make u the subject: u = (s - (1/2)at²) / t. Since we don't have acceleration yet, we'll assume the entire displacement occurred at the final velocity (v = 33 m/s) throughout the 4.3 seconds: u = (100 - (1/2) * 33 * 4.3) / 4.3. Calculating with these assumed values gives us an initial velocity. Then we use that initial velocity and final velocity to calculate acceleration using the first kinematic equation: a = (v - u) / t. Plugging the initial and final velocities, and time into this equation, we can find the car's acceleration.