How Is Acceleration Calculated in Uniform Acceleration Problems?

[TCleland]

Homework Statement

A drag car starting from rest and accelerating uniformly acquires a speed of 60 m/s while traveling a distance of 270m. Calculate the acceleration.

Homework Equations

No idea

The Attempt at a Solution

No idea

 

[edgepflow]

There is a very basic kinematic equation that relates everything in this problem together. Have another review of this section in your textbook.

 

[TCleland]

No textbook and no notes.

He just wanted us to answer this. Help anyone?

 

[edgepflow]

Then have a look at equations (1) to (5) in:

http://en.wikipedia.org/wiki/Equations_of_motion

Which one applies?

 

[rwisz]

I am happy to assist you with this problem. The equations that can be used to solve uniform acceleration problems are:

1. v = u + at (where v is final velocity, u is initial velocity, a is acceleration, and t is time)

2. s = ut + 1/2 at^2 (where s is distance, u is initial velocity, a is acceleration, and t is time)

Using the given information, we can rearrange equation 2 to solve for acceleration:

a = 2(s - ut) / t^2

Substituting the given values of s = 270m, u = 0 m/s, and t = unknown, we can solve for t:

60 m/s = 0 m/s + a(t)
60 m/s = at
t = 60 m/s / a

Substituting t = 60 m/s / a into the equation for acceleration, we get:

a = 2(270m - 0 m/s * 60 m/s / a) / (60 m/s / a)^2
a = 2(270m) / 3600 m^2/s^2
a = 0.15 m/s^2

Therefore, the acceleration of the drag car is 0.15 m/s^2. I hope this helps you understand how to solve uniform acceleration problems. Remember to always use the appropriate equations and units when solving problems in physics.