Velocity and Displacement: How to Derive Expressions from Acceleration Equation

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Homework Statement



The acceleration a ms^-2 of a car is given by a=18t - 4 where t is the time in seconds.Derive expressions for the velocity v ms^-1 and the displacement x m if the initial velocity and displacement are both zero

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The Attempt at a Solution


would really appreciate any help with this.I have no idea where to start!Trying to get a sample answer so i can study it to past exam paper questions
 
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Start with the definition of acceleration:

acceleration is the rate of change of velocity, so a= dv/dt.

If you replace 'a' by 'dv/dt' in your equation, can you find 'v'?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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