Distance, Velocity, and Acceleration

There is a relationship between distance, velocity and acceleration. When you understand how they interact, and their equations; they are much easier to grasp. The relationship between distance and velocity is proportional.
Distance = velocity x time
If acceleration is involved in the question, the equation becomes
Distance = v0 x t + 0.5 a t^2
Where v0 is original velocity.
With these two equations, you can solve almost every question.

Example

If a car goes 3m/s and it accelerates 2m/s^2 for 5 seconds. What is the distance the car went?
First, identify the values. a = 2,v0=3, and t=5
Now, substitute the value in the equation

D = 3 x 5 + 0.5 x 2 x 5^2
= 15 + 25
= 40

Like this you can simply apply the values in the equation.

Example 2

A car was going X m/s. It accelerates 4m/s^2 for 4 seconds. The total distance it went was 40m. What is X?
First, identify the values. a = 4,d=40, and t=4
Now, substitute the value in the equation
40 = v0 x 4 + 0.5 x 4 x 4^2
40=4v0 + 32
8 = 4v0
v0 = 2
=> X = 2m/s

 

Like this you can apply the equation and solve the question.

 

Example 3: An object falling.

Newton dropped an apple from 10m high. How long would it take for it to touch the ground if the acceleration is 9.81m/s^2?
First, identify the values. We know that v0 = 0 since it’s falling.

Also, a = 9.81m/s^2, d=10
Now, substitute the value in the equation

D = 0.5at^2
We know D = 10m, and a = 9.81m/s^2

10 = 0.5*9.81*t^2
t^2 = 5.095
t = 2.247seconds

 

Example 4:

Galileo dropped a feather from 20m high. The acceleration it falls is 4m/s^2. How long would it take for the feather to touch the ground?

First, identify the values. We know that v0 = 0 since it’s falling.
Also, a = 4m/s^2, d=20

Now, substitute the value in the equation
D = 0.5a*t^2
20=0.5*4*t^2
20=2t^2
t^2=10
t= 3.16s

Tutors for Physics are available if you need more help.

This article was written for you by Edmond, one of the tutors with SchoolTutoring Academy.

1,482 thoughts on “Distance, Velocity, and Acceleration”

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