Deceleration question

[Sophie]

Hello

I am stuck on the last part of a question and would appreciate some help creating a formula from the question to work out the antiderivatives.

A car going 70km/h come to a stop in 6 seconds. Assume that the decceleration is constant.

a. Graph the velocity against time.

b. Represent as an area on your graph, the distance travelled.

c. Find the distance travelled from your graph.

d. Using antiderivatives, find the distance travelled.

a. Ok I have a graph where x is time and y is velocity.
b. I have shaded the area under the graph to show the distance travelled.
c. Using the graph I worked out the area under the graph

(1/2)(70*(1/600)) = 7/120 km = 58.333m

d. Here is where I get stuck, I struggle to come up with an equation for velocity, which I can then use to find the position.

This is what I have attempted, but I am sure it is wrong.

V(t) = (1/600)t - (0)t

If somone can help me with the equation I would be very greatful

Thanks Sophie

 

[tkhunny]

There are no antiderivative to "work out". It is the same thing every time. Just plug in what you know.

Constant Acceleration: a(t) = a
Velocity: v(t) = a*t + b
Position: s(t) = (a/2)t^2 + bt + c

It's going when we first look at it.
v(0) = 70 km/h
b = 70 km/h

It stops
v(6) = 0 km/h
2a = -35 km/h

Essentially, we can ignore 'c'. why?

Where does that leave us?

 

[Sophie]

Thanks for the info

It has taken me a few days, but I went back to my texts re-did some examples and then came back to what you said. It now makes sense.

Thanks