What is the magnitude of the car’s displacement in meters, as it accelerates uniformly from a speed of 84 km/h to one of 104 km/h?

Question

A certain car is capable of accelerating at a uniform rate of 0.79 m/s2. What is the magnitude of the car’s displacement in meters, as it accelerates uniformly from a speed of 84 km/h to one of 104 km/h?

Answer 1

Use the kinematic relation

 

v_f² - v_i² = 2ax

 

v_i = 84 km/h = (84,000 m) /(3600 s) = 23.33 m/s

v_f = 104 km/h = (104,000 m)/(3600 s) = 28.89 m/s

 

a = 0.79 m/s²

 

x = distance = ?

 

x = (v_f² - v_i²)/(2a) = (28.89² - 23.33²)/[2(0.79)] m = 183.76 m