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A particle is moving in the with acceleration (2t - 3) ms^-2 and initial velocity 2ms^-1. Find the distance travelled when the velocity has reached 12ms^-1.

(1.) Integrate the expression for acceleration to find an expression for velocity: Velocity v = t^2 - 3t + c When t = 0, velocity = 2. Substituting in to find constant c, 2 = 0 + 0 + c therefore c = 2. v = t...
RF
Answered by Richard F. • Maths tutor
6885 Views

Differentiate the following function u = Cos(x3)

u = Cos(x 3 ) To differentiate this function we will use the chain rule. Firstly we will set x 3 to another variable name such as v. So now v = x 3 . Lets differentiate this. dv/dx = 3x 2 We can now differen...
SB
Answered by Serena B. • Maths tutor
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Differentiate y = 7(x)^2 + cos(x)sin(x)

This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rule: ...
EC
Answered by Edward C. • Maths tutor
4171 Views

Find the set of values of x for which x(x-4) > 12

When solving this quadratic inequality, we should use a three-step approach. The first step is to reformat the inequality to put one side equal to zero, which is the standard format of a quadratic equation. ...
DB
Answered by Daniel B. • Maths tutor
14605 Views

Simplify (5-2√3)/(√3-1) giving your answer in the form p +q√3, where p and q are rational numbers

The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the den...
AW
Answered by A W. • Maths tutor
21013 Views