Math Problem Solver

The equation for a distance, s meters (m), travelled in time t seconds (s) by an elevator starting with an initial velocity u meters per second (ms-1) and uniform acceleration a meters per second per second (ms-2) is:

Assignment title

Using calculus techniques to solve a construction problem

Purpose of this assignment:

Learners will be able to select and apply suitable mathematical techniques to solve practical construction problems.

Learning Aims: Learning Aim 2

Examine how calculus can be used to solve a construction problem.

Scenario:

You have been contracted as a mathematical consultant to solve and confirm a number of mathematical problems/solutions for projects on a major contract for the government, as explained below:

Task 1

The equation for a distance, s meters (m), travelled in time t seconds (s) by an elevator starting with an initial velocity u meters per second (ms-1) and uniform acceleration a meters per second per second (ms-2) is:

= +

If = − and = −:

a) create a suitable data table and hence draw a graph of distance s against time t for the first 5 seconds of motion.

2

BTEC Level 3 Diploma in Construction and the Built Environment

b) using your graph, determine an approximate value for the velocity of the object when = 3.

c) use a numerical method to calculate an approximate value of the velocity when t = 3s.

d) use differentiation from first principles to find the function for the velocity v when time t=3s (Hint: =

).

e) compare and comment on the methods used and results obtained in parts b, c and part d.

If = − and = −:

f) find the velocity and the acceleration a of the object when t=2s and when