Motion with constant acceleration

Motion with constant acceleration

Constant Acceleration

An object moves with constant acceleration when the velocity changes at the same rate every second.

For example, a constant 4m/s^2 acceleration means the velocity increases by 4m/s every second.

So far you have learned how to calculate average speed, average velocity, and average acceleration.

Now you are going to learn how to calculate displacement, change in time, final velocity, and initial velocity when the acceleration is uniform, or constant.

When the accelerating object has an initial velocity, use these formulas:

  $\left(1\right)\ \ \ \ \ \ \ \Delta x\ =\ \frac{1}{2}\left(vi\ +vf\right)\Delta t$  

 $\left(2\right)\ \ \ \ \ \ \ \ vf=vi+a\Delta t$  

 $\left(3\right)\ \ \ \ \ \ \ \ \Delta x=vi\Delta t\ +\ \frac{1}{2}a\left(\Delta t\right)^2$  

 $\left(4\right)\ \ \ \ \ \ \ \ \ vf^2=vi^{2\ }+\ 2a\Delta x$  

How do you know which formula to use?

It dependeds on what information you have.

If you are looking for displacement and you have vi, vf and change in time, use the first formula.

If you are looking for displacement and you have change in time and acceleration, use the third formula.

If you are looking for final velocity and you have vi, acceleration, and change in time, use the second formula.

If you looking for final velocity but you have vi, acceleration, and displacement, use the fourth formula.

If the accelerated object starts from rest, initial velocity equals zero, use these formulas:

 $\left(1\right)\ \ \ \ \ \Delta x=\ \frac{1}{2\ }vf\Delta t$  

 $\left(2\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ vf=a\Delta t$  

 $\left(3\right)\ \ \ \ \ \ \Delta x=\frac{1}{2}a\left(\Delta t\right)^2$  

 $\left(4\right)\ \ \ \ \ \ \ \ \ \ \ vf^2=2a\Delta x$  

Multiple Choice

A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500m/s^2. What is the velocity of the stroller after it has traveled 4.75m?

• 2.18m/s

• 3.2m/s

• 4.8m/s

• 5.12m/s

Open Ended

An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195m long. What is the minimum uniform acceleration required for a safe landing?

Multiple Choice

A certain car is capable of accelerating at a uniform rate of 0.85 m/s^2. What is the magnitude (numerical value) of the car's displacement as it accelerates uniformly from a speed of 83km/hr to 94km/hr?

• 109m

• 35 m

• 88m

• 79m