How do you find Acceleration when given Distance and Time?

Homework Statement

Data Collected on a Race by a Dragster
Distance (m) - 20.0 when Time (s) 0.945
Distance (m) - 400.0 when Times (s) 8.96
What is the acceleration of the dragster from the 20.0-m mark to the 400.0m mark?
(The answer book says 1.27m/s2 but i don't know how to get it )

Homework Equations

v=d/t
d= initial velocity*t+1/2at2

The Attempt at a Solution

v=20/0.945
v=21.16 m/s

(2(d-(initial velocity *t)))/t2 = a
(2(380-(21.16*8.02))/8.022 = a
(2*211.10)/64.32 = a
6.56m/s2

i know the reason why im doing this wrong is because im using average velocity instead of using the initial velocity but i don't know how to find instantaneous velocity without a graph and i have too little information to draw one

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Kurdt
Staff Emeritus
Gold Member
You also know that the dragster should have zero velocity at t = 0.

Using

$$d=\frac{Vo+Vf}{2}t$$

you can obtain the Vf, which is the velocity at the 20m mark, and its the initial velocity from the 20m to the 400m.

you can find the acceleration by finding the initial velocity (should be zero unless otherwise noted) and the final velocity. take and subtract the initial from the final and dived it by the change in time.