Acceleration and time

Question

A car accelerates from 14 m/s to 21 m/s in 6.0 s. What was its acceleration? How far did it travel in this time? Assume constant acceleration.

Answer 1

Since acceleration is constant, it will be equal to the change in velocity over change in time.

a = (21 - 14)/6 = 7/6 = 1.167 m/s²

For the distance traveled, we know that for constant acceleration,

x = x₀ + v₀t + 1/2 at²

This equation is obtained from integrating the equation d²x/dt² = a for constant acceleration.

If you are not familiar with calculus, don't worry about this.

From the equation for position assuming the initial position is 0, we have

x = 0 + 14(6) + (1/2)(7/6)(6²)

x = 105 m

So the acceleration is 1.167 m/s² and the total distance traveled in the 6 seconds is 105 m.