What car should you buy

Question

You are trying to buy a new car and want the one with the greatest acceleration. Car A can go from 0 to 60 mph in 3.8 seconds. Car B can travel a distance of 12.4 m in 1.94 s
when accelerating from rest. Car C can accelerate from 8 m/s to 24 m/s in a distance of 34.2 m. Calculate the acceleration of each car. Which car should you buy

Answer 1

Hello Gabby,

 

To solve this problem, you'll need three different equations relating acceleration to various other parameters. Keep a list of the equations you've learned so far, and see if you can find the correct equation for each car.

 

For Car A, you need to relate acceleration when you have the initial velocity, the final velocity, and the elapsed time. Find an equation that includes a, v_i, v_f, and t.

 

For Car B, you need acceleration when you have the initial velocity, the initial position, the final position, and the elapsed time. Find an equation that includes a, v_i, x_i, x_f, and t.

 

For Car C, you need acceleration when you have the initial velocity, the final velocity, and the distance traveled. Find an equation that uses a, v_i, v_f, and d (or Δx).

 

Still need help? Continue reading:

 

 

 

 

 

 

 

For Car A, use the definition of acceleration:

 

     a = (v_f - v_i)/t

 

For Car B, use the position equation with x_f = 12.4m and x_i = 0:

 

     x_f = x_i + v_it + (1/2)at²

 

For Car C, use the velocity-distance equation:

 

     v_f² = v_i² + 2ad

 

Hope this has helped!