another modelling question i cant get my head aroundWatch

#1
i need help with q

10) a cyclist is travelling along a straight road.the distance in metres of the cyclist from a fixed point after t seconds is modelled by the function f(t), where f'(t)=5+2t and f(0)=0
a) find expression for f(t)
b) calculate the time taken for the cyclist to travel to 100m

ive done part a) which is 5t+t^2+c

on part b) i have only concluded that we are asked to find f(100) and i have found that C is 0, becuase
f(0)=5(0)+(0)^2+c = 0,
i think im doing this wrong. someone help
0
3 weeks ago
#2
(Original post by 13.oswin.tsang)
i need help with q

10) a cyclist is travelling along a straight road.the distance in metres of the cyclist from a fixed point after t seconds is modelled by the function f(t), where f'(t)=5+2t and f(0)=0
a) find expression for f(t)
b) calculate the time taken for the cyclist to travel to 100m

ive done part a) which is 5t+t^2+c

on part b) i have only concluded that we are asked to find f(100) and i have found that C is 0, becuase
f(0)=5(0)+(0)^2+c = 0,
i think im doing this wrong. someone help

f is a function of time. Give it a time, and it tells you the distance from the starting point. You are told the distance from the starting point, and you need to find the time that goes with it. Does this help you to see what the equation you have to solve is?
0
3 weeks ago
#3
(Original post by 13.oswin.tsang)
i need help with q

10) a cyclist is travelling along a straight road.the distance in metres of the cyclist from a fixed point after t seconds is modelled by the function f(t), where f'(t)=5+2t and f(0)=0
a) find expression for f(t)
b) calculate the time taken for the cyclist to travel to 100m

ive done part a) which is 5t+t^2+c

on part b) i have only concluded that we are asked to find f(100) and i have found that C is 0, becuase
f(0)=5(0)+(0)^2+c = 0,
i think im doing this wrong. someone help
TBH, you haven't done part (A) completely. In this part of the question you need to determine the value of by using the initial condition .

You actually spilled this into part (B) where you are actually correct that .

So .

So finish off the question. We seek such that .

Have a go at it first but if you can't see a way to proceed then here's a hint:
Spoiler:
Show

You want to solve the equation for a solution . Notice that it's a quadratic equation, so it should be no trouble!
Last edited by RDKGames; 3 weeks ago
0
#4
thank you.
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