An auto starts from rest and accelerates at 3 m/s^2 for 54 seconds. How fast is it going after this acceleration? Express to the nearest m/s?

Question

An auto starts from rest and accelerates at 3 m/s^2 for 54 seconds. How fast is it going after this acceleration? Express to the nearest m/s?

Answer 1

You can use one of the kinematic equations of motion to solve this problem. Those equations are:

Δx = x_f - x_i

v_avg = ½ (v_f + v_i) = Δx / Δt

v_f = v_i + at

x_f = x_i + v_it + ½ at²

v_f² = v_i² + 2a(x_f − x_i)

In this case, since we are looking for velocity and we have the initial velocity (0, since the car was initially at rest) and we have the time (54 sec), and we have the acceleration (3 m/s²), we would use the third equation v_f = v_i + at

v_f = 0 + (3)(54) = 162 m/s