1989 Nov. G.C.E Homework

When a stone is thrown vertically upwards, it’s distance (d metres) after t seconds is given by the formula d=60t-10t². For values of t from 1 to 5 seconds using 2cm to 1unit on the t axis and 2cm to 20units on the d-axis. Calculate your graph

### (I) how long does it take to reach a height of 70 metres? (II) determine the height of the stone after 5 seconds (III) after how many seconds does it reach to it maximum height (IV) determine the slope of the graph when t = 5 seconds

Solution

Solution

First we’ve to find distance d(meters)

Formula d = 60t-10t²,

For values of t from 1 to 5 seconds

When t = 1

distance d (meters) = 60t-10t²

60(1)-10(1)² = 60-10

50( distance is 50 when time is 1 second)

When t = 2

distance d (meters) = 60t-10t²

60(2)-10(2)² = 120-10(4)

120-10×4 = 120-40

80( distance is 80 when time is 2 second)

When t = 3

distance d (meters) = 60t-10t²

60(3)-10(3)² = 180-10×9

180-90 = 90 ( distance is 90 when time is 3 second)

When t = 4

distance d (meters) = 60t-10t²

60(4)-10(4)² = 240-10×16

240-160 = 80( distance is 80 when time is 4 second)

When t=5

distance d (meters) = 60t-10t²

60(5)-10(5)² = 300-10×25

300-250 = 50 ( distance is 50 when time is 5 second)

Plot a graph of distance against time ( where distance(d metres) will be y axis and time ( t seconds) will represent x axis

Let y represent 20cm at 2units

And let X represent 1cm at 2units

How to plot graph of d(metres) against t (secs)

Watch this video